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é±ã®èµ°è¡è·é¢ = 1æ¥ãããã®èµ°è¡è·é¢ à é±ã®èµ°è¡æ¥æ°
é±ã®èµ°è¡è·é¢ = 12ãã€ã« à 5æ¥ = 60ãã€ã«
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èµ°è¡æé = ç·è·é¢ ÷ æé
èµ°è¡æé = 60ãã€ã« ÷ 10ãã€ã«/æ = 6æé
ãããã£ãŠããžã§ã€ã ãºã¯é±ã«6æéèµ°ãããšã«ãªããŸããçãã¯ã####6ãã§ãã
| 6
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èŠãªãªãŒã麊ã®è¢ã¯äœè¢ã§ããïŒ
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1é£ãããã®ãªãŒã麊æ¶è²» = 5ãã³ã à 4é = 20ãã³ã
圌ã¯1æ¥2åé€ãããã®ã§ã1æ¥ã«å¿
èŠãªãªãŒã麊ã®åèšã¯:
1æ¥ã®ãªãŒã麊æ¶è²» = 20ãã³ã à 2é£ = 40ãã³ã
5æ¥éã®å Žåã®ç·ãªãŒã麊æ¶è²»éã¯:
5æ¥éã®ãªãŒã麊æ¶è²» = 40ãã³ã à 5æ¥ = 200ãã³ã
1è¢ã®ãªãŒã麊ã¯50ãã³ããªã®ã§ãå¿
èŠãªè¢ã®æ°ã¯:
å¿
èŠãªè¢ã®æ° = 200ãã³ã ÷ 50ãã³ã/è¢ = 4è¢
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èŠãªãªãŒã麊ã®è¢ã®æ°ã¯4è¢ã§ããæçµçãªåçã¯ä»¥äžã®éãã§ãã
#### 4
| 4
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ãã¡ã©ãã¢ã³ã®æ°ã¯æ¬¡ã®ããã«èšç®ããŸãïŒ
\[
\frac{2}{3} \times 27 = 18
\]
ãããã£ãŠããžã£ãã¯18å¹ã®ãã¡ã©ãã¢ã³ã飌ã£ãŠããŸãã
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\[
\frac{1}{3} \times 18 = 6
\]
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æçµçãªçãã¯ã6å¹ã§ãã
åçïŒ####6
| 6
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|
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12ãã« - 4ãã« = 8ãã«
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8ã㫠÷ 2ãã«/æ¥ = 4æ¥
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| 4
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64å - 48å = 16åã®åµããã¬ã€ã«çœ®ããŸããã
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ãã¡ããªãŒãµã€ãºã®ãã¶ã®äŸ¡æ Œ = å°ããªãã¶ã®äŸ¡æ Œ à 3
= 8ãã« Ã 3
= 24ãã«
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= 8ãã« + 24ãã«
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1ã€ç®ã®äŒå Žã®è²»çšïŒAïŒã¯ä»¥äžã®ããã«ãªããŸãã
- åºæ¬æéïŒ200ãã«
- é£äºä»£ïŒåå è
1人ããã5ãã« Ã åå è
ã®æ° \( n \)
ãããã£ãŠã1ã€ç®ã®äŒå Žã®ç·è²»çšã¯æ¬¡ã®ããã«ãªããŸãã
\[ A = 200 + 5n \]
2ã€ç®ã®äŒå Žã®è²»çšïŒBïŒã¯ä»¥äžã®ããã«ãªããŸãã
- æéïŒåå è
1人ããã25ãã« Ã åå è
ã®æ° \( n \)
ãããã£ãŠã2ã€ç®ã®äŒå Žã®ç·è²»çšã¯æ¬¡ã®ããã«ãªããŸãã
\[ B = 25n \]
ãããã®è²»çšãçãããªããšãã® \( n \) ãæ±ããŸãã
\[ 200 + 5n = 25n \]
䞡蟺ãã \( 5n \) ãåŒããŸãã
\[ 200 = 25n - 5n \]
\[ 200 = 20n \]
䞡蟺ã20ã§å²ããŸãã
\[ n = \frac{200}{20} = 10 \]
ã€ãŸããåå è
ã10人ã®å Žåã«ã2ã€ã®äŒå Žã®è²»çšãçãããªããŸãã
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| 10
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- ãªãªãŒãèŠã€ããæè«ã®æ°ã \( L \)
- ãã€ããããèŠã€ããæè«ã®æ°ã \( D \)
- ããŒãã£ãèŠã€ããæè«ã®æ°ã \( B \)
äžããããæ¡ä»¶ãæ°åŒã§è¡šããŸãã
1. åèšã¯43å¹ïŒ
\[
L + D + B = 43
\]
2. ãªãªãŒã¯ãã€ããããã7å¹å€ãèŠã€ããïŒ
\[
L = D + 7
\]
3. ãã€ãããã¯ããŒãã£ãèŠã€ããæ°ã®ååïŒ
\[
D = \frac{1}{2} B \quad \Rightarrow \quad B = 2D
\]
ãããã®åŒã䜿ã£ãŠã倿° \( D \) ã䜿ã£ãŠè¡šçŸãçŽããŸãã
ãŸãã\( B \) ã \( D \) ã§è¡šããŸãïŒ
\[
B = 2D
\]
次ã«ã\( L \) ã \( D \) ã§è¡šããŸãïŒ
\[
L = D + 7
\]
ãããåèšã®åŒã«ä»£å
¥ããŸãïŒ
\[
(D + 7) + D + (2D) = 43
\]
æŽçããŸãïŒ
\[
4D + 7 = 43
\]
\[
4D = 36
\]
\[
D = 9
\]
ãã€ããããèŠã€ããæè«ã®æ° \( D \) ãåãã£ãã®ã§ããªãªãŒãšããŒãã£ã®æ°ãæ±ããŸãã
ãªãªãŒïŒ
\[
L = D + 7 = 9 + 7 = 16
\]
ããŒãã£ïŒ
\[
B = 2D = 2 \times 9 = 18
\]
æçµçã«ããªãªãŒãèŠã€ããæè«ã®æ°ã¯ 16 å¹ã§ãã
ãããã£ãŠããªãªãŒãèŠã€ããæè«ã®æ°ã¯ã#### 16ãã§ãã
| 16
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|
ãŸãããã©ã€ã¢ãšãã°ãã¡ããã䜿ã£ãæ¯ç³žã®éãèšç®ããŸãã
1. ãã©ã€ã¢ã䜿ã£ãæ¯ç³žã®éïŒ
ãã©ã€ã¢ã¯æ¯ç³žã®1/4çã䜿ããŸããã
æ¯ç³ž1çã¯364ã€ãŒããªã®ã§ããã©ã€ã¢ã䜿ã£ãéã¯
\[
\frac{1}{4} \times 364 = 91 \text{ã€ãŒã}
\]
2. ãã°ãã¡ããã䜿ã£ãæ¯ç³žã®éïŒ
ãã°ãã¡ããã¯æ¯ç³žã®1/2çã䜿ããŸããã
ãã°ãã¡ããã䜿ã£ãéã¯
\[
\frac{1}{2} \times 364 = 182 \text{ã€ãŒã}
\]
3. 圌女ãã¡ãåãããŠäœ¿ã£ãæ¯ç³žã®éïŒ
ãã©ã€ã¢ã91ã€ãŒãããã°ãã¡ããã182ã€ãŒãã䜿ã£ãã®ã§ãäºäººåãããŠäœ¿ã£ãéã¯
\[
91 + 182 = 273 \text{ã€ãŒã}
\]
ãããã£ãŠã圌女ãã¡ãåãããŠäœ¿ã£ãæ¯ç³žã®éã¯273ã€ãŒãã§ãã
æçµçãªåçã¯ã#### 273 ã§ãã
| 273
|
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¥ããããã«ãµãã©ã€ãºã§ã©ã³ãã ãªãã¬ãŒã³ãã10å远å ã§è²·ãããšã«ããŸããããã§ãªãŒã¯åèšã§äœåã®ãã¬ãŒã³ããè²·ããŸãããïŒ
|
ãã§ãªãŒã¯ãŸã5人ã®åéã®ããã«ãã¬ãŒã³ããè²·ããŸãã
- 2人ã®åéã¯ãããã5ã€ã®ãã¬ãŒã³ããæ¬²ããã£ãŠããã®ã§ã2 à 5 = 10åã§ãã
- æ®ãã®3人ã®åéã¯ãããã2ã€ã®ãã¬ãŒã³ããæ¬²ããã£ãŠããã®ã§ã3 à 2 = 6åã§ãã
ããããåèšãããšã
10 + 6 = 16åãšãªããŸãã
ããã«ããã§ãªãŒã¯ãµãã©ã€ãºã§10åã®ãã¬ãŒã³ãã远å ã§è³Œå
¥ããŸãã
åèšã¯ã
16 + 10 = 26åãšãªããŸãã
ãããã£ãŠããã§ãªãŒã賌å
¥ãããã¬ãŒã³ãã®ç·æ°ã¯26åã§ãã
åçã¯ã####26ãã§ãã
| 26
|
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à 2) + 2ãã£ãŒã
ãœãã¡ã®é·ã = (8ãã£ãŒã à 2) + 2ãã£ãŒã
ãœãã¡ã®é·ã = 16ãã£ãŒã + 2ãã£ãŒã = 18ãã£ãŒã
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åç: ####18
| 18
|
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1. ã€ããŽå³ã®ã¬ã ã®ããã¯ã®å€æ®µãxãã«ãšããŸãã
2. éãããå³ã®ã¬ã ã¯åé¡ã§ããã®äŸ¡æ Œãyãã«ãšããŸãã
å
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\[ 2x + 2 + \frac{y}{2} = 7 \]
éãããå³ã®ã¬ã ãå顿¯æãã§ããããšãèæ
®ãããšãåèšéé¡ã¯æ¬¡ã®ããã«è¡šçŸã§ããŸãã
ãŸãããããŠå³ã®ã¬ã ã®äŸ¡æ ŒãåŒããŸãã
\[ 2x + \frac{y}{2} = 7 - 2 = 5 \]
ä»ãyã¯éãããå³ã®ã¬ã ã®æ¬æ¥ã®äŸ¡æ Œã§ããéãããå³ã®ã¬ã ã®äŸ¡æ Œãæ±ãããã㫠暪軞ã®äŸ¡æ ŒãèããŸããéãããã¬ã ãxãã«ã«å¯Ÿããã®ã¯ä»¥äžã®ããã«èšå®ãããŸãã
\[ y = 2z \]
ããããèæ
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å ±ããã€ããŽã®äŸ¡æ Œãæ±ããŸããéãããã®ããã¯ã®äŸ¡æ Œã¯åãããªãã®ã§ãšããããåºå®å€ãšããŠã¿ããŸãã
åèšãåæ§æãããšïŒ
\[ 2x + \frac{z}{2} = 5 \]
ããã§ãã€ããŽå³ã®ã¬ã ã®å€æ®µã¯yã®2åã«ãªããããè£å®ã§:
ããy = 1ãã«ãšä»®å®ããå Žåãéãããå³ã®äŸ¡æ Œã¯2ãã«ããããåèšéé¡ãç¶æããŸãããããã£ãŠ1ãã«ãšããæ¡ä»¶äžã§åããŠããã£ãããã¹ãããããšãå¯èœã§ãã
ä»®ã«ãã€ããŽå³ãxã«ç¶ããšããŠãã®å®éã®è©äŸ¡ãå å³ãããã¹ãæçµçãªçµè«ïŒ
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2x=4
x=2
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çµè«ãšããŠãã€ããŽå³ã®ã¬ã 1ããã¯ã¯ $2 ã§ãã
ãããã£ãŠãã€ããŽå³ã®ã¬ã 1ããã¯ã®å€æ®µã¯ä»¥äžã®ããã«æ±ããããŸãã
#### 2
| 2
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|
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\[
\text{1æ¬ã®ã¹ãã£ãã¯ã®ã³ã¹ã} = \frac{4 \text{ãã«}}{200 \text{æ¬}} = 0.02 \text{ãã«/æ¬}
\]
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\[
\text{1æ¬ã®ã¹ãã£ãã¯ã®ã³ã¹ã} = \frac{6 \text{ãã«}}{400 \text{æ¬}} = 0.015 \text{ãã«/æ¬}
\]
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\text{賌å
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\]
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\[
\text{ã¹ãã£ãã¯ã®ç·æ°} = 4 \text{æ¬} \times 400 \text{æ¬/æ¬} = 1600 \text{æ¬}
\]
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\[
2 \text{ å/æ¥} \times 5 \text{ æ¥} = 10 \text{ å}
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\[
10 \text{ å} \times 2.20 \text{ ãã«/å} = 22 \text{ ãã«}
\]
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\[
22 \text{ ãã«} - 20 \text{ ãã«} = 2 \text{ ãã«}
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|
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- èŸ²å Žã®ç: 30é
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- åç©åã®ç: 60é
- åç©åã®çŸ: 20é
åèšã¯:
30 + 10 + 60 + 20 = 120é
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| 120
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|
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- çãã: 12å
- ããããã: 4å
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- çãã: \( 4x = 12 \)
- ããããã: \( 4y = 4 \)
ãããããããè§£ããŸãã
1. çããã®æ°:
\[
4x = 12 \implies x = \frac{12}{4} = 3
\]
2. ãããããã®æ°:
\[
4y = 4 \implies y = \frac{4}{4} = 1
\]
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\[
500 \times 0.20 = 100 \text{ãã«}
\]
2. æ®ã£ããéã¯ã500ãã«ããæã«äœ¿ã£ã100ãã«ãåŒãããã®ã§ãã
\[
500 - 100 = 400 \text{ãã«}
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3. 次ã«ãæ®ã£ããéã®25%ãCDã«äœ¿ããŸããæ®ã£ãŠãã400ãã«ã®25%ãèšç®ããŸãã
\[
400 \times 0.25 = 100 \text{ãã«}
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4. CDã«äœ¿ã£ã100ãã«ãæ®ã£ããéããåŒããŸãã
\[
400 - 100 = 300 \text{ãã«}
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| 375
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= 36 Ã (1/4)
= 36 ÷ 4
= 9æ
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= 18æ
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| 18
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10ãã«æã®åèš:
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20ãã«æã®åèš:
6æ Ã 20ãã« = 120ãã«
åãããŠãã¢ãªã®æã£ãŠãããéã®åèšã¯:
40ãã« + 120ãã« = 160ãã«
次ã«ãã¢ãªã¯æã£ãŠãããéã®ååã効ã«ãããŸãã
ååã¯:
160ã㫠÷ 2 = 80ãã«
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160ãã« - 80ãã« = 80ãã«
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3/5ã®éé¡ã¯:
80ãã« Ã (3/5) = 48ãã«
å€é£ã賌å
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80ãã« - 48ãã« = 32ãã«
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| 32
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ãããå®¶ã®å±æ ¹ã«çŠãæ·ãã®ã«2æéããããšãããããã€ã¹ã¯ããã®2åã®æéã«ããã«40åãå ããæéãããããŸãããã€ã¹ã¯äœåãããã§ããããïŒ
|
ãããå®¶ã®å±æ ¹ã«çŠãæ·ãã®ã«ãããæéã¯2æéã§ãããããåã«å€æãããšã2æé = 120åã§ãã
ãã€ã¹ããããæéã¯ãããã®æéã®2åã«40åãå ãããã®ã§ãããããã£ãŠã
ãã€ã¹ã®æé = 2 à ããã®æé + 40å
ãã€ã¹ã®æé = 2 à 120å + 40å
ãã€ã¹ã®æé = 240å + 40å
ãã€ã¹ã®æé = 280å
ãããã£ãŠããã€ã¹ã¯280åããããŸãã
åçïŒ####280
| 280
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šå¡åããµã€ãºã§ãã圌女ã¯ããããã®å«ã«åžœåãããã©ãŒãã»ãŒã¿ãŒãããã³ãéŽäžãäœããããšèããŠããŸããåžœåãäœãã®ã«æ¯ç³žã2çãããã©ãŒã«4çãã»ãŒã¿ãŒã«12çãããã³ã®ãã¢ã«1çãéŽäžã®ãã¢ã«2çå¿
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èŠãªæ¯ç³žã®éãèšç®ããŸãã
1. åžœåïŒ2ç à 3人 = 6ç
2. ããã©ãŒïŒ4ç à 3人 = 12ç
3. ã»ãŒã¿ãŒïŒ12ç à 3人 = 36ç
4. ããã³ã®ãã¢ïŒ1ç à 3人 = 3ç
5. éŽäžã®ãã¢ïŒ2ç à 3人 = 6ç
次ã«ãããããåèšããŸãã
åèš = 6ç + 12ç + 36ç + 3ç + 6ç = 63ç
ãããã£ãŠãããŒãµã¯63çã®æ¯ç³žãè²·ãå¿
èŠããããŸãã
åçïŒ####63
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ããŠããŸããåèšã§100åè§£ããªããã°ãªããŸãããæææ¥ã®å€ã«12åè§£ããŸãããç«ææ¥ã«ã¯æææ¥ã®3åã®æ°ãã€ãŸã36åãè§£ããŸãããæ°Žææ¥ã«ã¯æ®ãã®åé¡ã®4åã®1ãè§£ããŸãããæšææ¥ã«ã¯äœåã®æ°åŠã®åé¡ãè§£ããªããã°ãªããŸãããïŒ
|
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1. æææ¥ã«è§£ããå顿°: 12å
2. ç«ææ¥ã«è§£ããå顿°: 36å
3. åèšã§è§£ããå顿°: \(12 + 36 = 48\) å
æ°Žææ¥ã«ãæ®ãã®åé¡ã®4åã®1ãè§£ããªããã°ãªããŸãããæ®ãã®åé¡ã®æ°ã¯ä»¥äžã®ããã«èšç®ãããŸãã
4. æ®ãã®å顿°: \(100 - 48 = 52\) å
5. æ°Žææ¥ã«è§£ãå顿°: \( \frac{52}{4} = 13\) å
æšææ¥ã«è§£ããªããã°ãªããªãåé¡ã®èšç®ã¯æ¬¡ã®éãã§ãã
6. æšææ¥ã«å¿
èŠãªå顿°: æ®ãã®åé¡ - æ°Žææ¥ã«è§£ããåé¡
- æšææ¥ã«è§£ãå¿
èŠãããåé¡ã®ç·æ°ã¯:
\[
52 - 13 = 39 \text{å}
\]
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#### 39
| 39
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- ãããŒã¯1æéã«6ã¯ã©ãŒãã®ãã¡ããæã¿ãŸãã
- ãããŒã¯ãããŒããã1ã¯ã©ãŒãå°ãªãæãã®ã§ããããŒãæããã¡ãã®é㯠6 - 1 = 5 ã¯ã©ãŒãã§ãã
- ãã£ã·ãŒã¯ãããŒã®2åã®ãã¡ããæãã®ã§ããã£ã·ãŒãæããã¡ãã®é㯠5 à 2 = 10 ã¯ã©ãŒãã§ãã
- ãªãããŒã¯ãã£ã·ãŒãæããã¡ãããã2ã¯ã©ãŒãå°ãªãæãã®ã§ããªãããŒãæããã¡ãã®é㯠10 - 2 = 8 ã¯ã©ãŒãã§ãã
å
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ãã㌠+ ãã㌠+ ãã£ã·ãŒ + ãªãã㌠= 6 + 5 + 10 + 8 = 29 ã¯ã©ãŒã
ãããã£ãŠããããŒããããŒããªãããŒããã£ã·ãŒã1æéã«åèšã§æããã¡ãã®éã¯29ã¯ã©ãŒãã§ãã
ãããã£ãŠãçãã¯ã####29
| 29
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|
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93åïŒæïŒ + 39åïŒååŸïŒ = 132å
次ã«ãå£²ãæ®ã£ãŠãããã³ã®æ°ãèšç®ããŸãïŒ
200åïŒçŒãããã³ïŒ - 132åïŒå£²ãããã³ïŒ = 68å
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68åïŒæ®ã£ãŠãããã³ïŒ + 6åïŒè¿åããããã³ïŒ = 74å
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36æ¬ Ã· 6æ¬/å = 6å
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6å + 3å = 9å
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27ã«ãã ÷ 3 = 9ã«ãã
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9ã«ãã ÷ (3/4ã«ãã) = 9ã«ãã à (4/3) = 12å
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æ°ããããã€ã¹ã®æ¶è²»é: 2ããã¯ããæ
1æ¥ã®ç·æ¶è²»éïŒããã€ã¹è¿œå åŸïŒ:
12ããã¯ããæ + 2ããã¯ããæ = 14ããã¯ããæ
次ã«ã1é±éïŒ7æ¥éïŒã®æ¶è²»éãèšç®ããŸãã
çŸåšã®é±éã®é»æ°æ¶è²»é:
12ããã¯ããæ Ã 7æ¥ = 84ããã¯ããæ
æ°ããããã€ã¹è¿œå åŸã®é±éã®é»æ°æ¶è²»é:
14ããã¯ããæ Ã 7æ¥ = 98ããã¯ããæ
次ã«ã1ããã¯ããæãããã®æéãèæ
®ããŠã1é±éã®é»æ°æéãèšç®ããŸãã
çŸåšã®é±é黿°æé:
84ããã¯ããæ Ã 1.50ãã«/ããã¯ããæ = 126ãã«
æ°ããããã€ã¹è¿œå åŸã®é±é黿°æé:
98ããã¯ããæ Ã 1.50ãã«/ããã¯ããæ = 147ãã«
黿°æéã®å·®é¡ãèšç®ããŸã:
147ãã« - 126ãã« = 21ãã«
ãã®ãããã¢ãã®æ°ããããã€ã¹ã远å ããååŸã§ã®é±éã®é»æ°æéã®éãã¯21ãã«ã§ãã
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5人ã®å Žåãäœæ¥çã¯5人 à (1/10)è»/æ¥ = 5/10è»/æ¥ = 1/2è»/æ¥ã§ãã
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66 = x + 2
ããããããžã§ãã®ãœãã¡ã®æ°ãæ±ãŸããŸãïŒ
x = 66 - 2 = 64
ãããã£ãŠããžã§ãã®æã£ãŠãããœãã¡ã®æ°ã¯64åã§ãã
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ãªãã£ãŒãªã¢ã®æ€
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ãžã§ãã®ãœãã¡ = 64
ãžã§ãã®æ€
å = 66
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å) + (ãžã§ãã®ãœãã¡ + ãžã§ãã®æ€
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åèš = (20 + 22) + (64 + 66) = 42 + 130 = 172
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åºæ¬ã®ã¯ãŒã¯ã¢ãŠãæéïŒ
\[ 4 \text{æé/é±} \times 8 \text{é±é} = 32 \text{æé} \]
次ã«ã圌ãè¡ã£ãäŸå€çãªã¯ãŒã¯ã¢ãŠãã®æéãå ç®ããŸãã
1. 圌ã¯2é±é£ç¶ã§åé±5æéã®ã¯ãŒã¯ã¢ãŠããããŸããããã®éã¯éåžžã®4æéãè¶
ããŠããŸãã®ã§ã远å ã®æéã¯ïŒ
\[ (5 \text{æé} - 4 \text{æé}) \times 2 \text{é±} = 1 \text{æé} \times 2 = 2 \text{æé} \]
2. ãŸãã圌ã¯å¥ã®æã«1é±éã«6æéã¯ãŒã¯ã¢ãŠãããŸããããã®å Žåã®è¿œå ã®æéã¯ïŒ
\[ (6 \text{æé} - 4 \text{æé}) = 2 \text{æé} \]
ãããå
šãŠåèšãããšããžã§ã·ã¥ã®åèšã¯ãŒã¯ã¢ãŠãæéã¯æ¬¡ã®ããã«ãªããŸãã
\[ 32 \text{æé} + 2 \text{æé} + 2 \text{æé} = 36 \text{æé} \]
ãããã£ãŠããžã§ã·ã¥ã8é±éå
šäœã§ã¯ãŒã¯ã¢ãŠãã«è²»ãããåèšæéã¯36æéã§ããçãã¯æ¬¡ã®ãšããã§ãïŒ
#### 36
| 36
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1. æåã®åçæã§8人ãéããŸãã®ã§ãæ®ãã®äººæ°ã¯æ¬¡ã®ããã«ãªããŸãïŒ
\( 48 - 8 = 40 \) 人
2. éãã人æ°ã®5åã®äººæ°ããã¹ã«ä¹ããŸãã®ã§ãä¹ã人æ°ã¯ïŒ
\( 8 \times 5 = 40 \) 人
ãããå ãããšããã¹ã«ã¯æ¬¡ã®äººæ°ãä¹ã£ãŠããŸãïŒ
\( 40 + 40 = 80 \) 人
次ã«ã2çªç®ã®åçæã§é²ã¿ãŸãã
3. 2çªç®ã®åçæã§21人ãéããŸãã®ã§ãæ®ãã®äººæ°ã¯æ¬¡ã®ããã«ãªããŸãïŒ
\( 80 - 21 = 59 \) 人
4. éãã人æ°ã®3åã®1ã®äººæ°ãä¹ããŸãã®ã§ãä¹ã人æ°ã¯ïŒ
\( \frac{21}{3} = 7 \) 人
ãããå ãããšããã¹ã«ã¯æ¬¡ã®äººæ°ãä¹ã£ãŠããŸãïŒ
\( 59 + 7 = 66 \) 人
ãããã£ãŠã2çªç®ã®åçæã®åŸããã¹ã«ã¯66人ãä¹ã£ãŠããŸãã
æçµçãã¯ã####66
| 66
|
ãžã§ã€ã ã¯5幎åŸã«27æ³ã«ãªããŸãã8幎åŸã圌ã®ããšãã¯åœŒã®å¹Žéœ¢ã®2åãã5æ³è¥ããªããŸããçŸåšã2人ã®å¹Žéœ¢å·®ã¯äœæ³ã§ããïŒ
|
ãŸãããžã§ã€ã ã®çŸåšã®å¹Žéœ¢ãæ±ããŸãã5幎åŸã«27æ³ã«ãªãã®ã§ãçŸåšã®å¹Žéœ¢ã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
\[
27 - 5 = 22
\]
ãããã£ãŠãçŸåšãžã§ã€ã ã¯22æ³ã§ãã
次ã«ã8幎åŸã®ãžã§ã€ã ã®å¹Žéœ¢ãèšç®ããŸãã
\[
22 + 8 = 30
\]
8幎åŸã«ããšãã®å¹Žéœ¢ããžã§ã€ã ã®å¹Žéœ¢ã®2åãã5æ³è¥ããªããšããããšã¯ãããšãã®å¹Žéœ¢ã¯æ¬¡ã®ããã«è¡šããŸãã
\[
2 \times 30 - 5 = 60 - 5 = 55
\]
ãããã£ãŠã8幎åŸã«ããšãã¯55æ³ã§ãã
ãã®æãçŸåšã®ããšãã®å¹Žéœ¢ãèšç®ããããã«ã¯ã8幎åã®ããšãã®å¹Žéœ¢ãæ±ããŸãã
\[
55 - 8 = 47
\]
çŸåšã®ããšãã®å¹Žéœ¢ã¯47æ³ã§ãã
æåŸã«ããžã§ã€ã ãšããšãã®çŸåšã®å¹Žéœ¢å·®ãèšç®ããŸãã
\[
47 - 22 = 25
\]
ãããã£ãŠãçŸåšã®2人ã®å¹Žéœ¢å·®ã¯25æ³ã§ãã
æçµçãªçãã¯ä»¥äžã®éãã§ãã
#### 25
| 25
|
ãšããŒã«ã¯ã³ã³ãã¥ãŒã¿ãŒãã¢ãã¿ãŒ2å°ãããªã³ã¿ãŒãåãããŠ2,400ãã«ã§è³Œå
¥ããŸãããããªã³ã¿ãŒã®äŸ¡æ Œã¯ã³ã³ãã¥ãŒã¿ãŒãã400ãã«å®ãã£ãã§ããã³ã³ãã¥ãŒã¿ãŒã®äŸ¡æ Œã1,100ãã«ã ã£ãå Žåãã¢ãã¿ãŒ1å°ã®äŸ¡æ Œã¯ãããã§ããããïŒ
|
ãŸãããšããŒã«ã賌å
¥ããã¢ã€ãã ã®äŸ¡æ ŒãæŽçããŸãããã
- ã³ã³ãã¥ãŒã¿ãŒã®äŸ¡æ ŒïŒ\( 1,100 \)ãã«
- ããªã³ã¿ãŒã®äŸ¡æ ŒïŒ\( 1,100 - 400 = 700 \)ãã«
次ã«ããããã®äŸ¡æ ŒãçšããŠãã¢ãã¿ãŒã®åèšäŸ¡æ Œãæ±ããŸãããšããŒã«ã¯ãã³ã³ãã¥ãŒã¿ãŒãšããªã³ã¿ãŒããããŠã¢ãã¿ãŒ2å°ãåãããŠ\( 2,400 \)ãã«ã§è³Œå
¥ããŸããã
ã³ã³ãã¥ãŒã¿ãŒãšããªã³ã¿ãŒã®åèšäŸ¡æ Œãèšç®ããŸãïŒ
\[
1,100 + 700 = 1,800 \text{ãã«}
\]
次ã«ãã¢ãã¿ãŒ2å°ã®ç·äŸ¡æ Œãæ±ããŸãïŒ
\[
2,400 - 1,800 = 600 \text{ãã«}
\]
ã¢ãã¿ãŒ2å°ã®åèšã\( 600 \)ãã«ãªã®ã§ãã¢ãã¿ãŒ1å°ã®äŸ¡æ Œã¯ïŒ
\[
\frac{600}{2} = 300 \text{ãã«}
\]
ãããã£ãŠãã¢ãã¿ãŒ1å°ã®äŸ¡æ Œã¯300ãã«ã§ããæçµçãªçãã¯ä»¥äžã®éãã§ãã
#### 300
| 300
|
åŠæ ¡ã®é è¶³ã§20人ã®åäŸãã¡ãåºãããŸããã圌ããåå ããããã€ãã®æŽ»åã®äžã€ã§ãç·ã®åãšå¥³ã®åã«çããåãããããããããè²æ®»æ¢ãã®ã¹ã«ãã³ãžã£ãŒãã³ãã«åºãããŸãããç·ã®åãã¡ã¯æ¢ãã«è¡ã£ãŠããããã60åã®è²æ®»ãæã¡åž°ããŸããã女ã®åãã¡ãæã¡åž°ã£ãè²æ®»ã®æ°ããç·ã®åãã¡ãæã¡åž°ã£ãè²æ®»ã®æ°ã«ãã®4åãå ãããã®ãšçããå Žåãäžäººã®å¥³ã®åãæã¡åž°ã£ãè²æ®»ã¯ããã€ã§ããïŒ
|
ãã®åé¡ãè§£ãããã«ããŸãç·ã®åãšå¥³ã®åã®äººæ°ããããã \( b \) ãš \( g \) ãšããŸããå
ã«ãåäŸãã¡ã20人ãªã®ã§ã次ã®ãããªåŒãç«ãŠãããŸãã
\[
b + g = 20
\]
ããã§ã¯ç·ã®åãšå¥³ã®åãçããåãããããããç·ã®åãšå¥³ã®åã®äººæ°ã¯ãããã10人ã ãšèããããšãã§ããŸããããªãã¡ã
\[
b = g = 10
\]
ç·ã®åãã¡ã¯ãããã60åã®è²æ®»ãæã¡åž°ããŸããã®ã§ãç·ã®åãæã¡åž°ã£ãè²æ®»ã®åèšã¯ã
\[
\text{åèšè²æ®»} = 60 \times b = 60 \times 10 = 600
\]
女ã®åãã¡ãæã¡åž°ã£ãè²æ®»ã®æ°ããç·ã®åãã¡ãæã¡åž°ã£ãè²æ®»ã®æ°ã«4åãå ãããã®ãšçããå Žåã«ã€ããŠèããŸãã女ã®åãã¡ãæã¡åž°ã£ãè²æ®»ã®åèšã \( x \) ãšãããšã
\[
x = 600 + 4 \times 600 = 600 + 2400 = 3000
\]
女ã®åãæã¡åž°ã£ãè²æ®»ã®ç·æ°ã¯3000åã§ãã®ã§ãäžäººã®å¥³ã®åãæã¡åž°ã£ãè²æ®»ã®æ°ã¯ã
\[
\text{äžäººããã} = \frac{x}{g} = \frac{3000}{10} = 300
\]
ãããã£ãŠãäžäººã®å¥³ã®åãæã¡åž°ã£ãè²æ®»ã®æ°ã¯300åã§ãã
æçµçãªçãã¯æ¬¡ã®éãã§ãã
#### 300
| 300
|
ãžã§ãŒãžã5åã®ãã£ã³ãã£ãé£ã¹ãåŸããžã§ãŒãžã«ã¯3åã®ãã£ã³ãã£ãæ®ã£ãŠããŸããããã¯ã¯ãžã§ãŒãžã®ãã£ã³ãã£ã®æ°ã®2åãæã£ãŠããŸãããããã¯ã¯ããã€ã®ãã£ã³ãã£ãæã£ãŠããŸããïŒ
|
ãžã§ãŒãžã5åã®ãã£ã³ãã£ãé£ã¹ãåŸã«3åæ®ã£ãŠããã®ã§ãå
ã
ã®ãžã§ãŒãžã®ãã£ã³ãã£ã®æ°ã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
å
ã®æ° = æ®ã£ãŠããæ° + é£ã¹ãæ°
å
ã®æ° = 3 + 5 = 8
ããã¯ã¯ãžã§ãŒãžã®ãã£ã³ãã£ã®æ°ã®2åãæã£ãŠããã®ã§ãããã¯ã®ãã£ã³ãã£ã®æ°ã¯æ¬¡ã®ããã«ãªããŸãã
ããã¯ã®ãã£ã³ãã£ã®æ° = ãžã§ãŒãžã®ãã£ã³ãã£ã®æ° à 2
ããã¯ã®ãã£ã³ãã£ã®æ° = 8 à 2 = 16
ãããã£ãŠãããã¯ã¯16åã®ãã£ã³ãã£ãæã£ãŠããŸãã
åçïŒ####16
| 16
|
ãã§ããŒã¯10æ³ã§ããã¢ãªã¢ãã¯ãã§ããŒãã4æ³å¹Žäžã§ããã¢ãªã¢ããã2æ³å¹Žäžã®ã¢ã³ã¯äœæ³ã§ããããïŒ
|
ãã§ããŒã¯10æ³ã§ããã¢ãªã¢ãã¯ãã§ããŒãã4æ³å¹Žäžãªã®ã§ã
ã¢ãªã¢ãã®å¹Žéœ¢ = ãã§ããŒã®å¹Žéœ¢ - 4 = 10 - 4 = 6æ³ã§ãã
次ã«ãã¢ã³ã¯ã¢ãªã¢ããã2æ³å¹Žäžã§ãã®ã§ã
ã¢ã³ã®å¹Žéœ¢ = ã¢ãªã¢ãã®å¹Žéœ¢ + 2 = 6 + 2 = 8æ³ã§ãã
ãããã£ãŠãã¢ã³ã¯8æ³ã§ãã
åçã¯ïŒ####8
| 8
|
æåã®æ¬ã®åãã¯31mmã2çªç®ã®æ¬ã®åãã¯50mmã§ãã3çªç®ã®æ¬ã¯2çªç®ã®æ¬ããã5mmèãã4çªç®ã®æ¬ã¯æåã®æ¬ã®2åã®åãã§ãã4åã®æ¬ã®åèšã®åãã¯äœmmã§ããïŒ
|
æåã®æ¬ã®åãã¯31mmã§ãã
2çªç®ã®æ¬ã®åãã¯50mmã§ãã
3çªç®ã®æ¬ã¯2çªç®ã®æ¬ããã5mmèãã®ã§ã3çªç®ã®æ¬ã®åãã¯50mm - 5mm = 45mmã§ãã
4çªç®ã®æ¬ã¯æåã®æ¬ã®2åã®åããªã®ã§ã4çªç®ã®æ¬ã®åãã¯31mm à 2 = 62mmã§ãã
ããããã®æ¬ã®åããåèšãããšã
31mm + 50mm + 45mm + 62mm = 188mm ã«ãªããŸãã
ãããã£ãŠã4åã®æ¬ã®åèšã®åãã¯188mmã§ãã
åçã¯ã####188ãã§ãã
| 188
|
ãšãã¯1ã¶æã«72æ¬ã®åç»ãäœæããŠã¢ããããŒãã§ããŸããããããæåã®é±ã«ã¯18æ¬ã2é±ç®ã«ã¯21æ¬ã3é±ç®ã«ã¯15æ¬ã®åç»ããäœæã§ããŸããã§ããã圌女ã¯1ã¶æã«72æ¬ã®åç»ã宿ãããããã«ãããšäœæ¬ã®åç»ãäœæããå¿
èŠããããŸããïŒ
|
ãšãã1ã¶æã§äœæãããåç»ã®æ¬æ°ã¯72æ¬ã§ãã
圌女ãæåã®é±ã«äœæããåç»æ°ã¯18æ¬ã2é±ç®ã«ã¯21æ¬ã3é±ç®ã«ã¯15æ¬ã§ãããããè¶³ãåãããŠããããŸã§ã«äœæããåç»ã®æ¬æ°ãæ±ããŸãã
18 + 21 + 15 = 54
ãšãã¯çŸåš54æ¬ã®åç»ãäœæããŠããŸããåœŒå¥³ãææ«ãŸã§ã«å®æãããªããšãããªãåç»ã®æ¬æ°ã¯72æ¬ãã54æ¬ãåŒããæ°åã«ãªããŸãã
72 - 54 = 18
ãããã£ãŠããšãã¯ããš18æ¬ã®åç»ãäœæããå¿
èŠããããŸãã
åçã¯ã####18ãã§ãã
| 18
|
18ãã«ã3人ã®ç·ã®åã«åããããŸãããé·ç·ã¯èªåã®åã«5ãã«ã远å ããç¿æ¥ã«ããã«10ãã«ã远å ããŸããããã®åŸã圌ã¯ããããã®ãéãå¿
èŠã«ãªãããããŸã§ã®åèšãã8ãã«ã䜿ããŸãããããã«è²¯éããåŸã8ãã«ã䜿ã£ãåŸã«æ®ã£ãéé¡ã3åã«ããããšãã§ããŸããã圌ã¯ä»ããããæã£ãŠããŸããïŒ
|
ãŸãã18ãã«ã3人ã®ç·ã®åã§åããŸããåçã«åãããšã1人ãããã®éé¡ã¯ïŒ
18ã㫠÷ 3人 = 6ãã«
ãããã£ãŠãåç·ã®åã¯6ãã«ãåãåããŸãã
é·ç·ã¯èªåã®åã«5ãã«ã远å ããŸããã®ã§ã
6ãã« + 5ãã« = 11ãã«
次ã«ã圌ã¯ããã«10ãã«ã远å ããŸããã
11ãã« + 10ãã« = 21ãã«
ãã®åŸã圌ã¯8ãã«ã䜿ããŸããã
21ãã« - 8ãã« = 13ãã«
次ã«ã圌ã¯è²¯éããåŸãæ®ã£ãéé¡ã3åã«ããŸããã
13ãã« Ã 3 = 39ãã«
ãããã£ãŠãé·ç·ã仿ã£ãŠããéé¡ã¯39ãã«ã§ããæçµçãªåçã¯æ¬¡ã®ãšããã§ãã
#### 39
| 39
|
ãšã«ãã¹ã¯æ¯æ1,125ãã«ã®è²¯éç®æšãæã£ãŠããŸãã4æã«ã¯ãç®æšãéæããããã«ãæã®ååã«è²¯éããéé¡ã®2åãåŸåã§æ¯æ¥è²¯éããããšèããŠããŸããæã®åŸåã®åæ¥ã«åœŒã¯ããã貯éããå¿
èŠããããŸããïŒ
|
ãšã«ãã¹ã®è²¯éç®æšã¯æ¯æ1,125ãã«ã§ããæã®ååãšåŸåã§è²¯éããé¡ãèããŸãã
1. ãŸããæã®ååã«è²¯éããéé¡ã \( x \) ãšããŸãã
2. æã®åŸåã«è²¯éããéé¡ã¯ãååã®2åãªã®ã§ \( 2x \) ãšãªããŸãã
3. æã®ååã¯15æ¥éãåŸåã15æ¥éã§ãã
ãšã«ãã¹ã®è²¯éç®æšã®åŒã¯æ¬¡ã®éãã§ãïŒ
\[
x + 2x = 1125
\]
\[
3x = 1125
\]
ãã®åŒãè§£ããšã
\[
x = \frac{1125}{3} = 375
\]
ãããã£ãŠãæã®ååã«ã¯375ãã«ã貯éããŸãã
次ã«ãåŸåã«è²¯éããé¡\( 2x \)ãæ±ããŸãïŒ
\[
2x = 2 \times 375 = 750
\]
æã®åŸåã®åæ¥ã«è²¯éããéé¡ãæ±ããããã750ãã«ã15æ¥ã§å²ããŸãïŒ
\[
\frac{750}{15} = 50
\]
ãããã£ãŠããšã«ãã¹ã¯æã®åŸåã§æ¯æ¥50ãã«è²¯éããå¿
èŠããããŸãã
åçã¯ã####50ãã§ãã
| 50
|
ãŽã¡ãŒãã¯æç©ã倧奜ãã§ãã圌女ã¯ãªã³ãŽã1å1.50ãã«ã§3åããªã¬ã³ãžã1å0.80ãã«ã§5åãæ¡ã1å0.75ãã«ã§6åè²·ããŸããã圌女ã20ãã«æ¯æã£ãå Žåããé£ãã¯ãããã«ãªããŸããïŒ
|
ãŽã¡ãŒããæç©ã«æ¯æã£ãåèšéé¡ãèšç®ããŸãã
- ãªã³ãŽ: 1.50ãã« Ã 3å = 4.50ãã«
- ãªã¬ã³ãž: 0.80ãã« Ã 5å = 4.00ãã«
- æ¡: 0.75ãã« Ã 6å = 4.50ãã«
次ã«ãããããåèšããŸãïŒ
4.50ãã« (ãªã³ãŽ) + 4.00ãã« (ãªã¬ã³ãž) + 4.50ãã« (æ¡) = 13.00ãã«
ãŽã¡ãŒãã¯20ãã«æ¯æã£ãã®ã§ããé£ãã¯æ¬¡ã®ããã«èšç®ã§ããŸãïŒ
20ãã« - 13ãã« = 7ãã«
ãããã£ãŠããé£ãã¯7ãã«ã§ãã
çãã¯ã####7ã§ãã
| 7
|
ãžã£ã€ã©ã¹ã¯å°ããªã¿ã¹ã¯ã1ã€ããªãããšã«0.8ãã«ãããžã§ããŒã¯0.5ãã«ãããããŸãããã圌ãããããã20ã¿ã¹ã¯ãçµããå Žåããžã£ã€ã©ã¹ã¯ãžã§ããŒããã©ãã ãå€ãã®ãéããããã§ããããïŒ
|
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¥ã¯æ¬¡ã®ããã«ãªããŸãã
ãžã£ã€ã©ã¹ã®åå
¥ = 0.8ãã« Ã 20ã¿ã¹ã¯ = 16ãã«
äžæ¹ããžã§ããŒã¯1ã¿ã¹ã¯ããšã«0.5ãã«ããããã®ã§ã20ã¿ã¹ã¯ãçµããå Žåã®åå
¥ã¯æ¬¡ã®ããã«ãªããŸãã
ãžã§ããŒã®åå
¥ = 0.5ãã« Ã 20ã¿ã¹ã¯ = 10ãã«
次ã«ããžã£ã€ã©ã¹ããžã§ããŒããã©ãã ãå€ãã®ãéãããã£ãŠããããèšç®ããŸãã
ãžã£ã€ã©ã¹ã®åå
¥ - ãžã§ããŒã®åå
¥ = 16ãã« - 10ãã« = 6ãã«
ãããã£ãŠããžã£ã€ã©ã¹ã¯ãžã§ããŒããã6ãã«å€ãããããŸãã
çãã¯6ã§ãã####6
| 6
|
ãžã§ããšãã©ããã¯100ãã«ãåãåãããšããŠããŸãããžã§ãã¯ãã©ããã®4åã®éé¡ãåãåããŸãããžã§ãã¯ãããåãåãã§ããããïŒ
|
ãžã§ããåãåãéé¡ã \( J \) ãšãããã©ãããåãåãéé¡ã \( B \) ãšããŸããåé¡ã®æ¡ä»¶ã«ãããæ¬¡ã®2ã€ã®åŒãæãç«ã¡ãŸãã
1. \( J + B = 100 \) ïŒãžã§ããšãã©ããã®åèšéé¡ïŒ
2. \( J = 4B \) ïŒãžã§ãã¯ãã©ããã®4åïŒ
åŒ2ãåŒ1ã«ä»£å
¥ããŸãã
\[ 4B + B = 100 \]
ãããæŽçãããšã
\[ 5B = 100 \]
䞡蟺ã5ã§å²ããŸãã
\[ B = 20 \]
ãã©ããã®éé¡ã20ãã«ãªã®ã§ããžã§ãã®éé¡ã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
\[ J = 4B = 4 \times 20 = 80 \]
ãããã£ãŠããžã§ããåãåãéé¡ã¯80ãã«ã§ãã
çãïŒ80####
| 80
|
ãžã§ãã®è·å Žã¯3ãã€ã«é¢ããŠããŸãã圌ã¯åãæ¥ã¯æ¯æ¥åŸåŸ©ã§æ©ããŸããé±ã«5ååãå Žåã圌ã¯äœãã€ã«æ©ãããšã«ãªããŸããïŒ
|
ãžã§ãã®è·å Žã¯3ãã€ã«é¢ããŠããŸãã®ã§ãåŸåŸ©ã§ã®è·é¢ã¯æ¬¡ã®ããã«èšç®ã§ããŸãïŒ
åŸåŸ©ã®è·é¢ = 3ãã€ã«ïŒè¡ãïŒ + 3ãã€ã«ïŒåž°ãïŒ = 6ãã€ã«
é±ã«5ååãã®ã§ã1é±éã§ã®æ©ãè·é¢ã¯æ¬¡ã®ããã«èšç®ã§ããŸãïŒ
1é±éã®è·é¢ = 6ãã€ã«ïŒåŸåŸ©ïŒ à 5æ¥ = 30ãã€ã«
ãã£ãŠã圌ã1é±éã«æ©ãè·é¢ã¯30ãã€ã«ã§ãããããã£ãŠãåçãšãªãæ°åã¯ã####30ãã§ãã
| 30
|
ãšãªãŒãºã¯ã¢ã«ãã¡ãããã®æžãæ¹ãåŠãã§ããããããå®å
šã«èŠãããŸã§äœåºŠãæžãçŽãããšã«ããŸããã圌女ã¯ã¢ã«ãã¡ãããã2åå
šãŠæžããããã«1åã¯ååã ãæžãããã®åŸããã§ã«æžãããã®ãå
šãŠå床æžããŸãããšãªãŒãºã¯åèšã§äœæåæžããããšã«ãªããŸããïŒ
|
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ãšãªãŒãºã®æžãæ¹ã¯æ¬¡ã®éãã§ãïŒ
1. ã¢ã«ãã¡ãããã2åå
šãŠæžãïŒ26æå à 2 = 52æå
2. ã¢ã«ãã¡ãããã®ååïŒ13æåïŒãæžãïŒ13æå
3. ãã§ã«æžããå
šãŠãå床æžãïŒ52æå + 13æå = 65æå
åèšã¯æ¬¡ã®ããã«èšç®ããŸãïŒ
52æå + 13æå + 65æå = 130æå
ãããã£ãŠããšãªãŒãºãåèšã§æžããæåæ°ã¯130æåã§ãã
åçïŒ####130
| 130
|
ã¢ãªã¯äº¡ããªã£ãååã®å®¶æã芪æã«é£çµ¡ããããã«é»è©±é£çµ¡ç¶²ã䜿çšããŸãããã¢ãªã¯3ã€ã®å®¶æã«é»è©±ããããããšã«ããŸããããã®åŸãåå®¶æã¯å¥ã®3ã€ã®å®¶æã«é»è©±ãããããã®ããã»ã¹ãç¶ããŸãã4åç®ã®é»è©±ã©ãŠã³ãã§äœå®¶æãéç¥ãããã§ããããïŒ
|
ã¢ãªãæåã«é£çµ¡ããå®¶æãã第0åç®ããšãããã®åŸã®å®¶æãžã®é£çµ¡ã¯ä»¥äžã®ããã«ãªããŸãã
- 第0åç®ïŒã¢ãªïŒ: 1å®¶æ
- 第1åç®: ã¢ãªã3å®¶æã«é£çµ¡ãã â 3å®¶æ
- 第2åç®: åå®¶æããŸã3å®¶æã«é£çµ¡ãã â 3 à 3 = 9å®¶æ
- 第3åç®: åå®¶æã3å®¶æã«é£çµ¡ â 9 à 3 = 27å®¶æ
- 第4åç®: åå®¶æã3å®¶æã«é£çµ¡ â 27 à 3 = 81å®¶æ
ãããã£ãŠã4åç®ã®é»è©±ã©ãŠã³ãã§éç¥ãããå®¶æã®æ°ã¯81å®¶æã§ãã
æçµçãªåçã¯ã####81ããšãªããŸãã
| 81
|
ããŒã¯ã¯3ã¶æéäœèª¿ãæªããæ¯æ10ãã³ããã€äœéãæžããŸãããæçµçãªäœéã70ãã³ãã ã£ãå Žåã圌ã®åæäœéã¯äœãã³ãã§ãããïŒ
|
ããŒã¯ã¯3ã¶æéãæ¯æ10ãã³ããã€äœéãæžã£ãã®ã§ãåèšã§30ãã³ãïŒ10ãã³ã à 3ã¶æïŒäœéãæžå°ããŸãããæçµçãªäœéã70ãã³ãã§ããããšããã圌ã®åæäœéã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
åæäœé = æçµçãªäœé + æžå°ããäœé
åæäœé = 70ãã³ã + 30ãã³ã
åæäœé = 100ãã³ã
ãããã£ãŠãããŒã¯ã®åæäœéã¯100ãã³ãã§ãã
åç: ####100
| 100
|
ãã®åºã§ã¯åŠçšåã販売ããŠããŸããããŒãã¯1å1.50ãã«ããã³ã¯1æ¬0.25ãã«ãé»åã¯1å°12ãã«ã幟äœåŠã»ããã¯1ã»ãã10ãã«ã§è²©å£²ãããŠããŸãããããšã«ã¯å·¥åŠã®åŠçã§ã5åã®ããŒãã2æ¬ã®ãã³ã1å°ã®é»åã1ã»ããã®å¹ŸäœåŠã»ããã賌å
¥ããããšèããŠããŸããåºã¯è³Œå
¥ããå
šãŠã®ååã«å¯ŸããŠ10%ã®å²åŒãæäŸããŠããŸãããããšã«ã欲ããååãå
šãŠè³Œå
¥ããããã«ã¯ããããæ¯æãå¿
èŠããããŸããïŒ
|
ãŸããããããã®ååã«å¯ŸããäŸ¡æ Œãèšç®ããŸãã
- ããŒã: 5å à 1.50ãã« = 7.50ãã«
- ãã³: 2æ¬ Ã 0.25ãã« = 0.50ãã«
- é»å: 1å° Ã 12ãã« = 12.00ãã«
- 幟äœåŠã»ãã: 1ã»ãã à 10ãã« = 10.00ãã«
次ã«ããããã®åèšéé¡ãèšç®ããŸãã
åèš = 7.50ãã« + 0.50ãã« + 12.00ãã« + 10.00ãã« = 30.00ãã«
次ã«ãåºã¯å
šãŠã®è³Œå
¥ã«å¯ŸããŠ10%ã®å²åŒãæäŸããŠããŸãã®ã§ãå²åŒé¡ãèšç®ããŸãã
å²åŒé¡ = 30.00ãã« Ã 10% = 3.00ãã«
å²åŒåŸã®åèšéé¡ãèšç®ããŸãã
å²åŒåŸåèš = 30.00ãã« - 3.00ãã« = 27.00ãã«
ãããã£ãŠããããšã«ãå
šãŠã®ååã賌å
¥ããããã«æ¯æãå¿
èŠãããéé¡ã¯27.00ãã«ã§ãã
åç: ####27.00
| 27
|
ã«ãŒãªãŒã¯åéããã¡ããããããšæã£ãŠããŸãã圌女ã¯ãã³ããŒã¬ãŒã1ã€4ãã«ã§5ã€ãããããã©ã€ã1ããã¯0.30ãã«ã§10ããã¯ããã«ãŒãããªã³ã¯ã®çŒ¶ã1猶2ãã«ã§5猶泚æããŸããã50ãã«æãæž¡ããå Žåãã«ãŒãªãŒã¯ãããã®ãé£ããåãåãã§ããããïŒ
|
ãŸããåã¢ã€ãã ã®åèšéé¡ãèšç®ããŸãããã
ãã³ããŒã¬ãŒïŒ
- 1ã€ã®å€æ®µ = 4ãã«
- æ³šææ° = 5ã€
- åèš = 4ãã« Ã 5 = 20ãã«
ããããã©ã€ïŒ
- 1ããã¯ã®å€æ®µ = 0.30ãã«
- æ³šææ° = 10ããã¯
- åèš = 0.30ãã« Ã 10 = 3ãã«
ãã«ãŒãããªã³ã¯ã®çŒ¶ïŒ
- 1猶ã®å€æ®µ = 2ãã«
- æ³šææ° = 5猶
- åèš = 2ãã« Ã 5 = 10ãã«
次ã«ããããã®åèšéé¡ããã¹ãŠè¶³ããŸãïŒ
åèšéé¡ = ãã³ããŒã¬ãŒ + ããããã©ã€ + ãã«ãŒãããªã³ã¯
åèšéé¡ = 20ãã« + 3ãã« + 10ãã« = 33ãã«
åœŒå¥³ãæž¡ãã50ãã«æããåèšéé¡ãåŒããŸãïŒ
ãé£ã = 50ãã« - 33ãã« = 17ãã«
ãããã£ãŠãã«ãŒãªãŒããé£ããšããŠåãåãéé¡ã¯17ãã«ã§ãã
åç㯠17 #### ã§ãã
| 17
|
ã¢ã³ããã©ã2500ãã«çžåœã®ååã売ã£ãå Žåã圌女ã皌ãã éé¡ãèšç®ããŠãã ãããååã1000ãã«å売ããšã30%ã®ææ°æãããããŸãã1000ãã«ãè¶
ãã売äžã«ã¯ãããã«10%ã®ææ°æãå ç®ãããŸãã
|
ã¢ã³ããã©ã2500ãã«çžåœã®ååã売ã£ãå Žåã®ææ°æãèšç®ããŸãã
ãŸãã1000ãã«ãŸã§ã®éšåã«å¯Ÿããææ°æãèšç®ããŸãã
1. 1000ãã«ã«å¯Ÿããææ°æ:
1000ãã« Ã 30% = 300ãã«
次ã«ã1000ãã«ãè¶
ããéšåãèšç®ããŸãã2500ãã«ã®å£²äžãã1000ãã«ãåŒããšã1500ãã«ãæ®ããŸãããã®1500ãã«ã«å¯ŸããŠææ°æãèšç®ããŸãã
2. 1000ãã«ãè¶
ãã1500ãã«ã«å¯Ÿããææ°æ:
1500ãã« Ã 10% = 150ãã«
次ã«ãäž¡æ¹ã®ææ°æãåèšããŸãã
åèšææ°æ = 300ãã« (1000ãã«å) + 150ãã« (1000ãã«ãè¶
ããå)
åèšææ°æ = 300ãã« + 150ãã« = 450ãã«
ã¢ã³ããã©ã2500ãã«çžåœã®ååã売ã£ãå Žåã圌女ã皌ãã éé¡ã¯450ãã«ã§ãã
ãããã£ãŠãçãã¯ä»¥äžã®éãã§ãã
#### 450
| 450
|
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èŠãªæ°Žã®ããã«ã®æ°ãèšç®ããããšããŠããŸããåœŒã¯æåã«24æ¬å
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èŠããããŸããïŒ
|
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¥ãã®æ°Žã®ã±ãŒã¹ã2ã€æã£ãŠããŸãã
24æ¬ Ã 2ã±ãŒã¹ = 48æ¬
次ã«ã70人ã®ã²ã¹ããããŠã1人ããã2æ¬ã®æ°Žãçšæãããã®ã§ãå¿
èŠãªæ°Žã®æ¬æ°ãèšç®ããŸãã
70人 à 2æ¬ = 140æ¬
次ã«ããã«ãæã£ãŠããæ°Žã®æ¬æ°ïŒ48æ¬ïŒãå¿
èŠãªæ¬æ°ïŒ140æ¬ïŒããåŒããŸãã
140æ¬ - 48æ¬ = 92æ¬
ãããã£ãŠããã«ã¯è¿œå ã§92æ¬ã®æ°Žãè²·ãå¿
èŠããããŸãã
åçã¯ïŒ####92
| 92
|
æ°Žãå·ããæãã¬ã€ã¯1ãã€ã«ã16åã§æ³³ããŸããæ°Žãæž©ããæãã¬ã€ã¯1ãã€ã«ã2å以äžã®æéã«ããã«2åãå ããæéã§æ³³ããŸããæãæ¥ã«3ãã€ã«æ³³ãã®ã«ãå¯ãæ¥ã«æ¯ã¹ãŠã¬ã€ã¯ã©ãã ãé·ãæéãèŠããŸããïŒ
|
ã¬ã€ãå·ããæ°Žã§1ãã€ã«ãæ³³ãæéã¯16åã§ããããã«åºã¥ããŠã3ãã€ã«ãæ³³ãæéã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
å·ããæ°Žã§ã®æ³³ãæé:
1ãã€ã«ã®æé à 3ãã€ã« = 16å à 3 = 48å
次ã«ãæž©ããæ°Žã§ã®æ³³ãæéãèšç®ããŸããæž©ããæ°Žã§ã¯ãæ³³ãæéã¯å·ããæã®2å以äžã®æéã«ããã«2åãå ãããã®ã§ãã
å·ããæ°Žã§ã®æéã¯16åãªã®ã§ã2åã¯32åã«ãªããŸãããããã£ãŠãæž©ããæ°Žã§ã®æ³³ãæéã¯æ¬¡ã®ããã«ãªããŸãã
æž©ããæ°Žã§ã®æé = 32å + 2å = 34å
ãã®æž©ããæ°Žã§1ãã€ã«ãæ³³ãæéã䜿ã£ãŠã3ãã€ã«ãæ³³ãæéãèšç®ããŸãã
æž©ããæ°Žã§ã®æé:
1ãã€ã«ã®æé à 3ãã€ã« = 34å à 3 = 102å
次ã«ãå¯ãæ¥ã«æ¯ã¹ãŠãæãæ¥ã«ã©ãã ãé·ãæéããããããèšç®ããŸãã
æãæ¥ã«ãããæé - å¯ãæ¥ã«ãããæé:
102å - 48å = 54å
ãããã£ãŠãã¬ã€ã¯æãæ¥ã«å¯ãæ¥ã«æ¯ã¹ãŠ54åé·ãæ³³ãããšã«ãªããŸãã
æçµçãªçãã¯54ã§ãã
#### 54
| 54
|
ãžã§ã³ã¯åãããéã貯éããèšç»ãç«ãŠãŠããŸããåœŒã®æçµŠã¯2ãã«ã§ãé±ã«4æ¥ã1æ¥5æéåããŸãã圌ã80ãã«è²¯éãããå Žåãäœé±éãããã§ããããïŒ
|
ãžã§ã³ã®æé絊ã¯2ãã«ã§ãé±ã«4æ¥ã1æ¥5æéåãã®ã§ã1é±éã®åå
¥ãèšç®ããŸãã
1é±éã®åãæéã¯ïŒ
4æ¥ Ã 5æé = 20æé
ãããã£ãŠã1é±éã®åå
¥ã¯ïŒ
20æé Ã 2ãã« = 40ãã«
ãžã§ã³ã80ãã«è²¯éããããã«å¿
èŠãªé±æ°ã¯æ¬¡ã®ããã«èšç®ããŸãïŒ
80ã㫠÷ 40ãã«/é± = 2é±é
ãããã£ãŠããžã§ã³ã80ãã«ã貯éããã®ã«ãããæéã¯2é±éã§ããåçã¯ã#### 2ããšãªããŸãã
| 2
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|
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6ã€ã³ãã®ã³ãŒã«ãã«ããã³ã³ããµãã®éé¡ã¯ã次ã®ããã«èšç®ã§ããŸãïŒ
ã³ãŒã«ãã«ããã³ã³ããµãã®éé¡ = 40ãã« Ã 3 = 120ãã«
ãããã£ãŠãã©ã³ãã®åèšä»£ã¯æ¬¡ã®ããã«ãªããŸãïŒ
åèšä»£ = ãã£ãã·ã¥ãµã + ã³ãŒã«ãã«ããã³ã³ããµã
åèšä»£ = 40ãã« + 120ãã« = 160ãã«
ãããã£ãŠã仿¥ã®ãµããŠã§ã€ã§ã®ã©ã³ã代ã¯åèš160ãã«ã§ããåŸã£ãŠãåçã¯æ¬¡ã®éãã§ãïŒ
#### 160
| 160
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- 2ã€ã®ç©Žããããã¿ã³ã¯7åã§ãã
- æ®ãã®ãã¿ã³ã¯ \( 21 - 7 = 14 \) åã§ãããã¯4ã€ã®ç©ŽããããŸãã
ããããã®ãã¿ã³ã®ç©Žã®æ°ãèšç®ããŸãã
1. 2ã€ã®ç©Žããããã¿ã³ã®ç©Žã®åèšïŒ
\( 7 \text{å} \times 2 \text{穎} = 14 \text{穎} \)
2. 4ã€ã®ç©Žããããã¿ã³ã®ç©Žã®åèšïŒ
\( 14 \text{å} \times 4 \text{穎} = 56 \text{穎} \)
å
šãŠã®ãã¿ã³ã®ç©Žã®åèšã¯æ¬¡ã®ããã«ãªããŸãïŒ
\[ 14 \text{穎} + 56 \text{穎} = 70 \text{穎} \]
ãããã£ãŠãè¢ã®äžã®å
šãŠã®ãã¿ã³ã«ã¯åèšã§70åã®ç©ŽããããŸãã
åç㯠#### 70 ã§ãã
| 70
|
ãã£ã¢ã·ãŒã®ããã«ãŒã¯24ç«æ¹ã€ã³ãã§ããã¶ãã¯ã®ããã«ãŒã¯ãã£ã¢ã·ãŒã®ããã«ãŒã®ååã®å€§ããã§ããããŒã¿ãŒã®ããã«ãŒã¯ã¶ãã¯ã®ããã«ãŒã®1/4ã®å€§ããã§ããããŒã¿ãŒã®ããã«ãŒã¯äœç«æ¹ã€ã³ãã§ããïŒ
|
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ã¶ãã¯ã®ããã«ãŒã¯ãã£ã¢ã·ãŒã®ããã«ãŒã®ååã®å€§ããã§ãã®ã§ïŒ
ã¶ãã¯ã®ããã«ãŒ = 24 / 2 = 12ç«æ¹ã€ã³ã
ããŒã¿ãŒã®ããã«ãŒã¯ã¶ãã¯ã®ããã«ãŒã®1/4ã®å€§ããã§ãã®ã§ïŒ
ããŒã¿ãŒã®ããã«ãŒ = 12 / 4 = 3ç«æ¹ã€ã³ã
ãããã£ãŠãããŒã¿ãŒã®ããã«ãŒã¯3ç«æ¹ã€ã³ãã§ãã
åçã¯ã####3ãã§ãã
| 3
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ãããã·ã§ããã«ã¯6ã€ã®å°åç©çšã®ã±ãŒãžããããŸããã3ã€ã®ã±ãŒãžã«ã¯ãã ã¹ã¿ãŒã10å¹ãã€ãæ®ãã®3ã€ã®ã±ãŒãžã«ã¯ã¢ã«ã¢ããã5å¹ãã€å
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|
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ãã ã¹ã¿ãŒã®åèš = 3ã±ãŒãž à 10å¹/ã±ãŒãž = 30å¹
ã¢ã«ã¢ããã¯3ã€ã®ã±ãŒãžã«ãããã5å¹ãã€ããã®ã§ãã¢ã«ã¢ããã®åèšã¯ä»¥äžã®ããã«èšç®ã§ããŸãã
ã¢ã«ã¢ããã®åèš = 3ã±ãŒãž à 5å¹/ã±ãŒãž = 15å¹
å
šäœã®å°åç©ã®åèšã¯ããã ã¹ã¿ãŒãšã¢ã«ã¢ãããè¶³ãåããããã®ã§ãã
åèš = ãã ã¹ã¿ãŒã®åèš + ã¢ã«ã¢ããã®åèš
åèš = 30å¹ + 15å¹ = 45å¹
ãããã£ãŠããããã·ã§ããã«ã¯åèšã§45å¹ã®å°åç©ãããŸããã
åçã¯ã####45ãã§ãã
| 45
|
ããŒã¯ã®äœéã¯150ãã³ãã§ãã¹ãŒã¶ã³ã®äœéã¯ããŒã¯ãã20ãã³ã軜ãã§ãããããŠã圌ãã®å人ã®ããã®äœéã¯ã¹ãŒã¶ã³ã®2åã§ãã3人ã®å人ã®å¹³åäœéã¯äœãã³ãã§ããããïŒ
|
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ããŒã¯ã®äœéã¯150ãã³ãã§ãã¹ãŒã¶ã³ã¯ããŒã¯ãã20ãã³ã軜ãã®ã§ã
ã¹ãŒã¶ã³ã®äœé = ããŒã¯ã®äœé - 20ãã³ã
= 150ãã³ã - 20ãã³ã
= 130ãã³ã
次ã«ãããã®äœéãèšç®ããŸãã
ããã¯ã¹ãŒã¶ã³ã®2åã®äœéãªã®ã§ã
ããã®äœé = ã¹ãŒã¶ã³ã®äœé à 2
= 130ãã³ã à 2
= 260ãã³ã
3人ã®å人ã®å¹³åäœéãæ±ããŸããå¹³åäœéã¯ãå
šå¡ã®äœéã®åèšã人æ°ã§å²ã£ããã®ã§ãã
å
šå¡ã®äœéã®åèš = ããŒã¯ã®äœé + ã¹ãŒã¶ã³ã®äœé + ããã®äœé
= 150ãã³ã + 130ãã³ã + 260ãã³ã
= 540ãã³ã
åäººã®æ°ã¯3人ãªã®ã§ãå¹³åäœéã¯æ¬¡ã®ããã«èšç®ããŸãã
å¹³åäœé = å
šå¡ã®äœéã®åèš / 人æ°
= 540ãã³ã / 3
= 180ãã³ã
ãããã£ãŠã3人ã®å人ã®å¹³åäœéã¯180ãã³ãã§ãã
åçã¯ã####180
| 180
|
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|
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4. æ°ããã«ãŒããããæ·ãè²»çšïŒ
1å¹³æ¹ãã£ãŒãããã34ãã«ãªã®ã§ã
æ·ãè²»çš = 34ãã« Ã 216å¹³æ¹ãã£ãŒã = 7,344ãã«
ãã¹ãŠã®è²»çšãåèšããŸãïŒ
åèšè²»çš = ã«ãŒãããã®è²»çš + ãããã®è²»çš + åãé€ãè²»çš + æ·ãè²»çš
åèšè²»çš = 2,592ãã« + 432ãã« + 864ãã« + 7,344ãã«
åèšè²»çš = 11,232ãã«
ãããã£ãŠããã€ã±ã«ãæ¯æãè²»çšã¯11,232ãã«ã§ãã
åç: ####11232
| 11,232
|
ããã¯ã¯ç©ãæ°ããããšã«èå³ãæã¡ã次ã®1é±éã§ç©ºã«ããé³¥ã®æ°ãæ°ããããšã«ããŸããã1æ¥ç®ãš2æ¥ç®ã®åèšã§50矜ã®é³¥ãèŠãŸããã3æ¥ç®ã«ã¯é³¥ãäžçŸœãèŠãŸããã§ããã4æ¥ç®ãš5æ¥ç®ã«ã¯120矜ã®é³¥ãèŠãŸããã6æ¥ç®ã«ã¯20矜ã7æ¥ç®ã«ã¯90矜ã®é³¥ãèŠãŸãããããã¯ã1æ¥å¹³åã§èŠãé³¥ã®æ°ã¯ããã€ã§ããïŒ
|
ãŸããããã¯ã1é±éïŒ7æ¥éïŒã«èŠãé³¥ã®æ°ãåèšããŸãã
1æ¥ç®ãš2æ¥ç®ã®åèšã¯50矜ã
3æ¥ç®ã¯0矜ã
4æ¥ç®ãš5æ¥ç®ã®åèšã¯120矜ã
6æ¥ç®ã¯20矜ã
7æ¥ç®ã¯90矜ã
ããããè¶³ãåããããšïŒ
50 (1æ¥ç®ãš2æ¥ç®) + 0 (3æ¥ç®) + 120 (4æ¥ç®ãš5æ¥ç®) + 20 (6æ¥ç®) + 90 (7æ¥ç®) = 280矜
次ã«ã1æ¥å¹³åã§èŠãé³¥ã®æ°ãæ±ããŸãã7æ¥éã§280矜èŠãã®ã§ã1æ¥å¹³åã¯æ¬¡ã®ããã«èšç®ããŸãã
280矜 ÷ 7æ¥ = 40矜/æ¥
ãããã£ãŠãããã¯ã1æ¥å¹³åã§èŠãé³¥ã®æ°ã¯40ã§ãã
åçã¯ã####40
| 40
|
ãã€ã¢ã³ã¯æ°åã«20ãšããåæå€ãäžããŸããããã®åæå€ã«ãã®æ°ã®ååãå ãããã®ã5ã§å²ãããã®çµæã«åæå€ãã12ãåŒããå€ãæããŸãããæ°åã®æçµçãªå€ã¯ããã€ã§ããããïŒ
|
ãŸãããã€ã¢ã³ãæ°åã«äžããåæå€ã20ãšããŸãã
1. åæå€ã«ãã®æ°ã®ååãå ããŸãïŒ
\[
20 + \frac{20}{2} = 20 + 10 = 30
\]
2. 次ã«ããã®çµæã5ã§å²ããŸãïŒ
\[
\frac{30}{5} = 6
\]
3. åæå€ãã12ãåŒããå€ãèšç®ããŸãïŒ
\[
20 - 12 = 8
\]
4. æåŸã«ã5ã§å²ã£ãçµæã«ããã®å€ãæããŸãïŒ
\[
6 \times 8 = 48
\]
ãããã£ãŠãæ°åã®æçµçãªå€ã¯48ã§ãã
åçã¯ã####48
| 48
|
ãã®ç·ã®åã¯5æã®ã«ãŒããæã£ãŠããŸãã圌ã®å
åŒã¯åœŒãã3æå°ãªãã«ãŒããæã£ãŠããŸãã圌ãã¯åãããŠäœæã®ã«ãŒããæã£ãŠããŸããïŒ
|
ãã®ç·ã®åã¯5æã®ã«ãŒããæã£ãŠããŸãã圌ã®å
åŒã¯åœŒãã3æå°ãªãã«ãŒããæã£ãŠããã®ã§ã圌ã®å
åŒã¯5 - 3 = 2æã®ã«ãŒããæã£ãŠããŸãã
圌ããåãããŠæã£ãŠããã«ãŒãã®ææ°ã¯ã5 + 2 = 7æã§ãã
ãã£ãŠã圌ãåãããŠæã£ãŠããã«ãŒãã®ææ°ã¯7æã§ããçãã¯####7ã§ãã
| 7
|
ããã¯ã¹ã¯ä»é±æ«ã«2æ¬ã®æ ç»ã芳ãäºå®ã§ãã1æ¬ç®ã®æ ç»ã¯1æé30åã2æ¬ç®ã®æ ç»ã¯2æé5åã®é·ãã§ããããã¯ã¹ã2æ¬ã®æ ç»ã芳ãã®ã«ãããæéã¯åèšäœåã§ããïŒ
|
1æ¬ç®ã®æ ç»ã®é·ãã¯1æé30åã§ãã®ã§ããããåã«æç®ãããš:
1æé = 60åãªã®ã§ã
1æé30å = 60å + 30å = 90å
2æ¬ç®ã®æ ç»ã®é·ãã¯2æé5åã§ãã®ã§ããããåã«æç®ãããš:
2æé = 120åãªã®ã§ã
2æé5å = 120å + 5å = 125å
äž¡æ¹ã®æ ç»ã®é·ããåèšãããš:
90å + 125å = 215å
ãããã£ãŠãããã¯ã¹ã2æ¬ã®æ ç»ã芳ãã®ã«ãããæéã¯åèš215åã§ãã
åçã¯####215ã§ãã
| 215
|
ããŒãã®å®¶ã®äŸ¡æ Œã¯76,000ãã«ã§ããããããã¢ã³ã®å®¶ãããŒãã®å®¶ãã30%å®ãå Žåã2è»ã®å®¶ã®åèšäŸ¡å€ãèšç®ããŠãã ããã
|
ãŸãããã¢ã³ã®å®¶ã®äŸ¡æ Œãèšç®ããŸãã
ããŒãã®å®¶ã®äŸ¡æ Œã¯76,000ãã«ã§ãããã¢ã³ã®å®¶ã¯ããŒãã®å®¶ãã30%å®ãã®ã§ããã¢ã³ã®å®¶ã®äŸ¡æ Œã¯æ¬¡ã®ããã«æ±ããŸãã
ãã¢ã³ã®å®¶ã®äŸ¡æ Œ = ããŒãã®å®¶ã®äŸ¡æ Œ - (ããŒãã®å®¶ã®äŸ¡æ Œ à 30%)
= 76,000ãã« - (76,000ãã« Ã 0.30)
= 76,000ãã« - 22,800ãã«
= 53,200ãã«
次ã«ã2è»ã®å®¶ã®åèšäŸ¡å€ãèšç®ããŸãã
åèšäŸ¡å€ = ããŒãã®å®¶ã®äŸ¡æ Œ + ãã¢ã³ã®å®¶ã®äŸ¡æ Œ
= 76,000ãã« + 53,200ãã«
= 129,200ãã«
ãããã£ãŠã2è»ã®å®¶ã®åèšäŸ¡å€ã¯129,200ãã«ã§ãã
åç: ####129200
| 129,200
|
ãžã¥ãã£ã¯æäŒã®ãã£ãªãã£ãŒã€ãã³ãã«æã£ãŠããããã«ãã«ããã1ããŒã¹ïŒ12åïŒãšãã«ããã®2åã®æ°ã®ç¿ã賌å
¥ããŸãããã€ãã³ãã§ã圌女ã®å人ã40åã®ã«ãããšããžã¥ãã£ãæã£ãŠããæ°ããã20åå€ãç¿ãæã£ãŠããããšãããããŸããã2人ãæã£ãŠããé£åšã®åèšæ°ã¯ããã€ã§ããïŒ
|
ãžã¥ãã£ã賌å
¥ããã«ããã®æ°ã¯1ããŒã¹ã§12åã§ãããã®ãããç¿ã®æ°ã¯ã«ããã®2åã§ãããããç¿ã®æ°ã¯ä»¥äžã®ããã«èšç®ã§ããŸãã
ç¿ã®æ° = 2 à 12 = 24å
ãžã¥ãã£ãæã£ãŠããé£åšã®åèšæ°ã¯ã«ãããšç¿ãè¶³ããæ°ã§ãã
ãžã¥ãã£ã®æã£ãŠããé£åšã®åèšæ° = 12 (ã«ãã) + 24 (ç¿) = 36å
次ã«ãå人ãæã£ãŠããé£åšã®æ°ãèããŸããå人ã¯40åã®ã«ãããšããžã¥ãã£ãæã£ãŠããç¿ã®æ°ããã20åå€ãç¿ãæã£ãŠããŸããã
å人ãæã£ãŠããç¿ã®æ° = 24 + 20 = 44å
åäººã®æã£ãŠããé£åšã®åèšæ°ã¯ã圌女ã®ã«ãããšç¿ã®åèšã§ãã
åäººã®æã£ãŠããé£åšã®åèšæ° = 40 (ã«ãã) + 44 (ç¿) = 84å
æåŸã«ã2人ãæã£ãŠããé£åšã®åèšæ°ãèšç®ããŸãã
åèšæ° = ãžã¥ãã£ã®é£åšã®åèšæ° + å人ã®é£åšã®åèšæ°
åèšæ° = 36 + 84 = 120
ãããã£ãŠã2人ãæã£ãŠããé£åšã®åèšæ°ã¯120åã§ãã
åçïŒ####120
| 120
|
1ç®±ã«ã¯90æã®äœ¿ãæšãŠã³ã³ã¿ã¯ãã¬ã³ãºãå
¥ã£ãŠãããããŒãã¯45æ¥é䜿çšã§ããŸãã1ç®±ã®äŸ¡æ Œã¯100ãã«ã§ãçŸåš10%ãªãã®ã»ãŒã«äžã§ãã圌ã2箱賌å
¥ããå Žåã1çµã®ã³ã³ã¿ã¯ãã¬ã³ãºã®ã³ã¹ãã¯ãããã«ãªããŸããïŒ
|
ãŸãã1ç®±ã®ã³ã³ã¿ã¯ãã¬ã³ãºã®äŸ¡æ Œãèšç®ããŸããçŸåš10%ãªãã®ã»ãŒã«äžã§ãã®ã§ã以äžã®ããã«èšç®ããŸãïŒ
1ç®±ã®äŸ¡æ Œ = 100ãã«
å²åŒé¡ = 100ãã« Ã 10% = 10ãã«
å²åŒåŸã®äŸ¡æ Œ = 100ãã« - 10ãã« = 90ãã«
次ã«ã2箱賌å
¥ãããšïŒ
2ç®±ã®äŸ¡æ Œ = 90ãã« Ã 2 = 180ãã«
1ç®±ã«ã¯90æã®ã¬ã³ãºãå
¥ã£ãŠããã®ã§ã2ç®±ã«ã¯ïŒ
90æ à 2 = 180æã®ã¬ã³ãºãå
¥ã£ãŠããŸãã
1çµã®ã³ã³ã¿ã¯ãã¬ã³ãºã¯éåžž2æã§ãããããã£ãŠã180æã®ã¬ã³ãºããåŸãããçµã®æ°ã¯ïŒ
180æ ÷ 2æ/çµ = 90çµ
æåŸã«ã1çµã®ã³ã³ã¿ã¯ãã¬ã³ãºã®ã³ã¹ããèšç®ããŸãïŒ
1çµã®ã³ã¹ã = 180ã㫠÷ 90çµ = 2ãã«
ãããã£ãŠã1çµã®ã³ã³ã¿ã¯ãã¬ã³ãºã®ã³ã¹ãã¯2ãã«ã§ãã
ãããã£ãŠãåçã¯ã####2ãã§ãã
| 2
|
ãã³ãã¯æ¶è²»ããã«ããªãŒ200ã«ããªãŒããšã«100mlã®æ°Žã飲ãå¿
èŠããããŸãã圌女ã¯2æéã®ãšã¢ããã¯ã¹ã§1æéããã500ã«ããªãŒãæ¶è²»ãã1æéã®ã©ã³ãã³ã°ã§1æéããã600ã«ããªãŒãæ¶è²»ããŸãã圌女ã¯äœmlã®æ°Žã飲ãå¿
èŠããããŸããïŒ
|
ãã³ãã¯ãšã¢ããã¯ã¹ãšã©ã³ãã³ã°ãåãããŠäœã«ããªãŒãæ¶è²»ããããèšç®ããŸãã
1. ãšã¢ããã¯ã¹ã§ã®æ¶è²»ã«ããªãŒ:
- 2æéã®ãšã¢ããã¯ã¹ã§1æéããã500ã«ããªãŒãæ¶è²»ããŸãã
- 2æé à 500ã«ããªãŒ/æé = 1000ã«ããªãŒ
2. ã©ã³ãã³ã°ã§ã®æ¶è²»ã«ããªãŒ:
- 1æéã®ã©ã³ãã³ã°ã§1æéããã600ã«ããªãŒãæ¶è²»ããŸãã
- 1æé à 600ã«ããªãŒ/æé = 600ã«ããªãŒ
3. åèšæ¶è²»ã«ããªãŒ:
- 1000ã«ããªãŒ (ãšã¢ããã¯ã¹) + 600ã«ããªãŒ (ã©ã³ãã³ã°) = 1600ã«ããªãŒ
4. æ¶è²»ã«ããªãŒã«å¯Ÿããæ°Žã®å¿
èŠé:
- 200ã«ããªãŒããšã«100mlã®æ°Žã飲ãå¿
èŠããããŸãã
- 1600ã«ããªãŒ ÷ 200ã«ããªãŒ = 8
- 8 Ã 100ml = 800ml
ãããã£ãŠããã³ãã¯800mlã®æ°Žã飲ãå¿
èŠããããŸãã
åç: ####800
| 800
|
ããŒã¬ãŒãã¬ã¹ã¬ã¹ãã©ã³ã«ã¯ãèµ€ãéãç·ã®ãžã§ãªãŒããŒã³ãºãå
¥ã£ã巚倧ãªç¶ããããŸããç¶ã®å€åŽã«ã¯ããã®ç¶ã«ã¯ãéããžã§ãªãŒããŒã³ãºããã1%å°ãªãèµ€ããžã§ãªãŒããŒã³ãºãšãéããžã§ãªãŒããŒã³ãºããã1%å€ãç·ã®ãžã§ãªãŒããŒã³ãºãå«ãŸããŠããŸãããšæžãããã¡ã¢ããããŸããç¶ã«ã¯åèšã§4500åã®ãžã§ãªãŒããŒã³ãºãå«ãŸããŠããå Žåãç·ã®ãžã§ãªãŒããŒã³ãºã¯èµ€ããžã§ãªãŒããŒã³ãºããäœåå€ãã§ããïŒ
|
èµ€ããžã§ãªãŒããŒã³ãºã®æ°ã \( R \)ãéããžã§ãªãŒããŒã³ãºã®æ°ã \( B \)ãç·ã®ãžã§ãªãŒããŒã³ãºã®æ°ã \( G \) ãšããŸãã
äžããããæ
å ±ãããæ¬¡ã®é¢ä¿åŒãç«ãŠãããŸãïŒ
- ç·æ°ã®é¢ä¿åŒïŒ
\[ R + B + G = 4500 \]
- èµ€ããžã§ãªãŒããŒã³ãºãéããžã§ãªãŒããŒã³ãºãã1%å°ãªããšããããšã¯ïŒ
\[ R = B - 0.01B = 0.99B \]
- ç·ã®ãžã§ãªãŒããŒã³ãºãéããžã§ãªãŒããŒã³ãºãã1%å€ããšããããšã¯ïŒ
\[ G = B + 0.01B = 1.01B \]
ãã®3ã€ã®åŒã䜿ã£ãŠããŸã \( R \) ãš \( G \) ã \( B \) ã«çœ®ãæããŸãããŸã \( R \) ãš \( G \) ãæ±ããŸãïŒ
\[ R = 0.99B \]
\[ G = 1.01B \]
ãããç·æ°ã®åŒã«ä»£å
¥ããŸãïŒ
\[ 0.99B + B + 1.01B = 4500 \]
ãã¹ãŠã \( B \) ã«ãŸãšãããšïŒ
\[ (0.99 + 1 + 1.01)B = 4500 \]
\[ 3B = 4500 \]
\[ B = \frac{4500}{3} = 1500 \]
次ã«ã \( B \) ã䜿ã£ãŠ \( R \) ãš \( G \) ãæ±ããŸãïŒ
\[ R = 0.99 \times 1500 = 1485 \]
\[ G = 1.01 \times 1500 = 1515 \]
æåŸã«ãç·ã®ãžã§ãªãŒããŒã³ãºãèµ€ããžã§ãªãŒããŒã³ãºããäœåå€ãããèšç®ããŸãïŒ
\[ G - R = 1515 - 1485 = 30 \]
ãããã£ãŠãç·ã®ãžã§ãªãŒããŒã³ãºã¯èµ€ããžã§ãªãŒããŒã³ãºãã30åå€ãã§ãã
åçã¯ã#### 30
| 30
|
ãžã£ã¬ããã¯ã¿ã€ãã³ã°é床ãäžããããšããŠããŸããåœŒã¯æåã1åéã«47èªã®é床ã§ãããããã€ãã®ã¬ãã¹ã³ãåããåŸã次ã«åœŒãã¿ã€ãã³ã°é床ããã¹ããããšããããã¯52èª/åã«å¢å ããŠããŸããããã圌ãããã«5èªåã¿ã€ãã³ã°é床ãäžããå Žåã3åã®æž¬å®ã®å¹³åã¯ããã€ã«ãªããŸããïŒ
|
ãžã£ã¬ããã®ã¿ã€ãã³ã°éåºŠã®æž¬å®å€ã¯æ¬¡ã®éãã§ãïŒ
1. æåã®é床ïŒ47èª/å
2. 次ã®é床ïŒ52èª/å
3. æåŸã®é床ïŒããã«5èªå¢å ããå ŽåïŒïŒ52 + 5 = 57èª/å
ãã®3ã€ã®é床ã®å¹³åãèšç®ããŸãã
å¹³å = (47 + 52 + 57) / 3
èšç®ãè¡ããŸãïŒ
47 + 52 + 57 = 156
ãã®åŸã156ã3ã§å²ããŸãïŒ
156 / 3 = 52
ãããã£ãŠã3åã®æž¬å®ã®å¹³åã¯52èª/åã§ããæçµçãªåçã¯ïŒ
#### 52
| 52
|
ããŒãã£ã³ãæ¯æ¥ã®æé£ã«ãã§ãªãªã¹ãé£ã¹ããšãé±ã«1.25ãã³ãæžéããŸããããæ¯æ¥ã®æé£ã«ããŒãããé£ã¹ããšãé±ã«1.75ãã³ãå¢éããŸãã5é±éåŸã2ã€ã®æé£ãªãã·ã§ã³ã«ããäœéã®å·®ã¯ã©ããããã«ãªããŸããïŒ
|
ããŒãã£ã³ããã§ãªãªã¹ãé£ã¹ãå Žåã®5é±éã§ã®äœéã®å€åã¯ã以äžã®ããã«èšç®ã§ããŸãã
1é±éã§ã®æžé = 1.25ãã³ã
5é±éã§ã®æžé = 1.25ãã³ã à 5é±é = 6.25ãã³ã
次ã«ãããŒãã£ã³ãããŒãããé£ã¹ãå Žåã®5é±éã§ã®äœéã®å€åãèšç®ããŸãã
1é±éã§ã®å¢é = 1.75ãã³ã
5é±éã§ã®å¢é = 1.75ãã³ã à 5é±é = 8.75ãã³ã
äž¡æ¹ã®æé£ãªãã·ã§ã³ã«ããäœéã®å·®ãèšç®ããŸãã
äœéã®å·® = ããŒããã«ããå¢é - ãã§ãªãªã¹ã«ããæžé
äœéã®å·® = 8.75ãã³ã + 6.25ãã³ã = 15ãã³ã
ãããã£ãŠã5é±éåŸã®2ã€ã®æé£ãªãã·ã§ã³ã«ããäœéã®å·®ã¯15ãã³ãã§ãã
åçã¯ã#### 15ãã§ãã
| 15
|
ç£å»ã®åŸ
å宀ã§4å¹ã®ç¬ãäžåã«åº§ã£ãŠããŸãããæåã®ç¬ã¯ã¢ãŒãã§ã³ãã³ã·ã£ãŒã§ãäœéã¯ãã£ãã®10ãã³ãã§ããããã®é£ã«åº§ã£ãŠããã®ã¯ããã¯ã¹ãã³ãã§ãã¢ãŒãã§ã³ãã³ã·ã£ãŒã®2åã®äœéã§ãããããã¯ã¹ãã³ãã®é£ã«åº§ã£ãŠããã®ã¯ãããšã³ã§ãããã¯ã¹ãã³ãã®äœéã®4åã®1ã§ããããããŠãåã®æåŸã«åº§ã£ãŠããã®ã¯ãã¹ãã£ãã§ããããšã³ã®äœéã®44åã§ããããã¹ãã£ãã®äœéã¯äœãã³ãã§ãããïŒ
|
ããã§ã¯ãç¬ã®ããããã®äœéãèšç®ããŸãããã
1. ã¢ãŒãã§ã³ãã³ã·ã£ãŒã®äœéã¯10ãã³ãã§ãã
- ã¢ãŒãã§ã³ãã³ã·ã£ãŒ = 10ãã³ã
2. ããã¯ã¹ãã³ãã¯ã¢ãŒãã§ã³ãã³ã·ã£ãŒã®2åã®äœéã§ãã
- ããã¯ã¹ãã³ã = 2 à 10ãã³ã = 20ãã³ã
3. ãããšã³ã¯ããã¯ã¹ãã³ãã®äœéã®4åã®1ã§ãã
- ãããšã³ = 20ãã³ã / 4 = 5ãã³ã
4. ãã¹ãã£ãã¯ãããšã³ã®äœéã®44åã§ãã
- ãã¹ãã£ã = 5ãã³ã à 44 = 220ãã³ã
ãããã£ãŠããã¹ãã£ãã®äœéã¯220ãã³ãã§ãããããã£ãŠãçãã¯ä»¥äžã®éãã§ãã
#### 220
| 220
|
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eBayã®ããŒãã®äŸ¡æ ŒïŒ13ãã«
eBayã®éæã¯Amazonã®2åã§ããããïŒ4ãã« Ã 2 = 8ãã«
eBayã§ã®ç·è²»çš = 13ãã« + 8ãã« = 21ãã«
æåŸã«ãeBayã§ã®ããŒãã®ç·è²»çšãAmazonããã©ãã ãé«ãããèšç®ããŸãã
eBayã§ã®ç·è²»çš - Amazonã§ã®ç·è²»çš = 21ãã« - 20ãã« = 1ãã«
ãããã£ãŠãeBayã§ã®ããŒãã®ç·è²»çšã¯Amazonãã1ãã«é«ããªããŸãã
åç: ####1
| 1
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ããŒã¯ã¯2éã®çªã®äžã«è±ã®æšãæ€ããŸããããã®çªã¯å°é¢ãã20ãã£ãŒãã®é«ãã«ãããŸããè±ã®æšã¯æ¯æ¥ãã®é«ãã2åã«ããŸããè±ã®æšãæå4ãã£ãŒãã®é«ãã§ãã£ãå ŽåãããŒã¯ã®çªãããé«ããªãã®ã«äœæ¥ããããŸããïŒ
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è±ã®æšã®åãã®é«ãã¯4ãã£ãŒãã§ããæ¯æ¥ããã®é«ãã¯2åã«ãªããŸããããŒã¯ã®çªã®é«ãã¯20ãã£ãŒãã§ãã
è±ã®æšã®é«ãã¯æ¬¡ç¬¬ã«æ¬¡ã®ããã«ãªããŸãïŒ
- Day 0: 4ãã£ãŒã
- Day 1: 4 à 2 = 8ãã£ãŒã
- Day 2: 8 à 2 = 16ãã£ãŒã
- Day 3: 16 à 2 = 32ãã£ãŒã
è±ã®æšãããŒã¯ã®çªã®é«ãïŒ20ãã£ãŒãïŒãè¶
ããã®ã¯Day 3ã®æã§ãã4ãã£ãŒãããå§ãŸãã3æ¥ç®ã«ã¯32ãã£ãŒããŸã§æé·ããŸãã
ãããã£ãŠãããŒã¯ã®çªãããé«ããªãã®ã«ãããæ¥æ°ã¯3æ¥ã§ãã
çãã¯ã####3
| 3
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ããã·ã¥ã«ãŒã 1ã«ããã¯100ã°ã©ã ã§ãã¿ã³ãã¯è³ªã3ã°ã©ã å«ãŸããŠããŸãããžã§ã³ãæ¯æ¥200ã°ã©ã ã®ããã·ã¥ã«ãŒã ãé£ã¹ãå Žåã1é±éã§åœŒã¯äœã°ã©ã ã®ã¿ã³ãã¯è³ªãæåããã§ããããïŒ
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ãžã§ã³ãæ¯æ¥200ã°ã©ã ã®ããã·ã¥ã«ãŒã ãé£ã¹ãå ŽåããŸã1ã«ããïŒ100ã°ã©ã ïŒããã3ã°ã©ã ã®ã¿ã³ãã¯è³ªãå«ãŸããŠããããšããã200ã°ã©ã ã®ããã·ã¥ã«ãŒã ã«å«ãŸããã¿ã³ãã¯è³ªãèšç®ããŸãã
1ã«ããïŒ100ã°ã©ã ïŒã§3ã°ã©ã ã®ã¿ã³ãã¯è³ªãªã®ã§ã200ã°ã©ã ã§ã¯æ¬¡ã®ããã«ãªããŸãïŒ
- 200ã°ã©ã ã®ããã·ã¥ã«ãŒã ã¯ã100ã°ã©ã ã2ã«ããã«çžåœããŸãã
ãããã£ãŠãã¿ã³ãã¯è³ªã¯æ¬¡ã®ããã«èšç®ã§ããŸãïŒ
- 3ã°ã©ã ïŒ100ã°ã©ã ãããïŒ Ã 2 = 6ã°ã©ã
ã€ãŸãããžã§ã³ã¯1æ¥ããã6ã°ã©ã ã®ã¿ã³ãã¯è³ªãæåããŸãã
1é±éïŒ7æ¥ïŒã§æåããã¿ã³ãã¯è³ªã¯ïŒ
- 6ã°ã©ã à 7æ¥ = 42ã°ã©ã
ãã£ãŠããžã§ã³ã1é±éã§æåããã¿ã³ãã¯è³ªã®éã¯42ã°ã©ã ã§ãã
åç: ####42
| 42
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ãžã§ãªãŒã¯5幎åã®2åã®å¹Žéœ¢ã§ãã3幎åŸããžã§ãªãŒã¯äœæ³ã«ãªããŸããïŒ
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ãŸãããžã§ãªãŒã®çŸåšã®å¹Žéœ¢ã x ãšããŸãã
5幎åã®ãžã§ãªãŒã®å¹Žéœ¢ã¯ x - 5 ã§ãã
ãã®å¹Žéœ¢ã®2åã¯ãžã§ãªãŒã®çŸåšã®å¹Žéœ¢ã«çããã®ã§ã次ã®åŒãæãç«ã¡ãŸãã
\[ x - 5 = \frac{x}{2} \]
ãã®æ¹çšåŒãè§£ããŠãããŸãã
䞡蟺ã«2ãæãããšïŒ
\[ 2(x - 5) = x \]
\[ 2x - 10 = x \]
次ã«xãå·ŠåŽã«ãŸãšããŸãã
\[ 2x - x = 10 \]
\[ x = 10 \]
ã€ãŸãããžã§ãªãŒã¯çŸåš10æ³ã§ãã
3幎åŸã®å¹Žéœ¢ã¯ïŒ
\[ 10 + 3 = 13 \]
ãããã£ãŠããžã§ãªãŒã¯3幎åŸã«13æ³ã«ãªããŸãã
åçã¯ã####13ãã§ãã
| 13
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ãžã§ãŒãžã¯æ¯ç§æ²»çè²»ãæ¯æãå¿
èŠããããŸãã圌ã¯ã€ã³ãã©ã³ãã2ã€å¿
èŠãšããŠããŸããåã€ã³ãã©ã³ãã®åºæ¬äŸ¡æ Œã¯2000ãã«ã§ããã€ã³ãã©ã³ãã®1ã€ã«ã¯ãç£åšè£œã®ã¯ã©ãŠã³ãã€ããããšèããŠããããã®è¿œå æ©èœã¯500ãã«ã®è²»çšãããããŸãã圌ã¯ãã§ã«600ãã«ã®é éãæ¯æã£ãŠããŸãã圌ã®ä»äºã§ã¯æçµŠ15ãã«ã§ããæ¯ç§æ²»çè²»ãæ¯æãã®ã«å¿
èŠãªåŽåæéã¯äœæéã§ããïŒ
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ãŸãããžã§ãŒãžãå¿
èŠãªæ¯ç§æ²»çã«ãããç·è²»çšãèšç®ããŸãã
1. ã€ã³ãã©ã³ã2ã€ã®åºæ¬äŸ¡æ Œ:
- ã€ã³ãã©ã³ã1ã€ã®äŸ¡æ Œ = 2000ãã«
- 2ã€ã®ã€ã³ãã©ã³ãã®äŸ¡æ Œ = 2000ãã« Ã 2 = 4000ãã«
2. ç£åšè£œã®ã¯ã©ãŠã³ã®è¿œå è²»çš:
- 500ãã«
3. ç·è²»çš:
- ç·è²»çš = ã€ã³ãã©ã³ãã®äŸ¡æ Œ + ã¯ã©ãŠã³ã®è¿œå è²»çš
- ç·è²»çš = 4000ãã« + 500ãã« = 4500ãã«
4. ãžã§ãŒãžãæ¢ã«æ¯æã£ãé é:
- 600ãã«
5. æ®ãã®æ¯æãã¹ãéé¡:
- æ®ãã®éé¡ = ç·è²»çš - é é
- æ®ãã®éé¡ = 4500ãã« - 600ãã« = 3900ãã«
6. åœŒã®æçµŠ:
- 15ãã«/æé
7. æŽçããŠãåŽåæéãæ±ããŸã:
- å¿
èŠãªåŽåæé = æ®ãã®éé¡ Ã· æçµŠ
- å¿
èŠãªåŽåæé = 3900ã㫠÷ 15ãã«/æé = 260æé
ãããã£ãŠããžã§ãŒãžãæ¯ç§æ²»çè²»ãæ¯æãã®ã«å¿
èŠãªåŽåæéã¯260æéã§ãã
#### 260
| 260
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äžè§åœ¢ã®3ã€ã®è§åºŠã®åèšã¯180床ã§ãã1ã€ã®è§åºŠã¯æå°ã®è§åºŠã®2åããã1ã€ã®è§åºŠã¯æå°ã®è§åºŠã®3åã§ããäžè§åœ¢ã®æå€§ã®è§åºŠã¯äœåºŠã§ããïŒ
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äžè§åœ¢ã®3ã€ã®è§åºŠããããã\( x \)ã\( 2x \)ã\( 3x \)ãšããŸããããã§ã\( x \)ã¯æå°ã®è§åºŠã§ãã
äžè§åœ¢ã®è§åºŠã®åèšã¯180床ã§ãã®ã§ã次ã®ãããªæ¹çšåŒãæãç«ã¡ãŸãã
\[
x + 2x + 3x = 180
\]
ãããè§£ããšã
\[
6x = 180
\]
䞡蟺ã6ã§å²ããšã
\[
x = 30
\]
ãããã£ãŠãããããã®è§åºŠã¯ä»¥äžã®ããã«ãªããŸãã
- æå°ã®è§åºŠ: \( x = 30 \)床
- 2åã®è§åºŠ: \( 2x = 60 \)床
- 3åã®è§åºŠ: \( 3x = 90 \)床
äžè§åœ¢ã®æå€§ã®è§åºŠã¯90床ã§ãã
æçµçãªçãã¯ãæå€§ã®è§åºŠã¯90床ã§ãã®ã§ãçãã¯ä»¥äžã®éãã§ãã
#### 90
| 90
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ã³ã«ããŒã¯1å5ã»ã³ãã®ã¬ã ããŒã«ãããã€ãè²·ããããšæã£ãŠããŸãã圌ãæã£ãŠããã®ã¯ã25ã»ã³ã硬貚ã8æã10ã»ã³ã硬貚ã6æã5ã»ã³ã硬貚ã14æããããŠ1ã»ã³ã硬貚ã15æã§ãã圌ã¯äœåã®ã¬ã ããŒã«ãè²·ãããšãã§ããã§ããããïŒ
|
ã³ã«ããŒãæã£ãŠãã硬貚ã®ç·é¡ãèšç®ããŸãã
- 25ã»ã³ã硬貚: 8æ à 25ã»ã³ã = 200ã»ã³ã
- 10ã»ã³ã硬貚: 6æ à 10ã»ã³ã = 60ã»ã³ã
- 5ã»ã³ã硬貚: 14æ à 5ã»ã³ã = 70ã»ã³ã
- 1ã»ã³ã硬貚: 15æ à 1ã»ã³ã = 15ã»ã³ã
ããããåèšããŸãã
200ã»ã³ã + 60ã»ã³ã + 70ã»ã³ã + 15ã»ã³ã = 345ã»ã³ã
ã¬ã ããŒã«ã®äŸ¡æ Œã¯5ã»ã³ãã§ãã®ã§ãã³ã«ããŒãè²·ããã¬ã ããŒã«ã®æ°ãèšç®ããŸãã
345ã»ã³ã ÷ 5ã»ã³ã = 69å
ãããã£ãŠãã³ã«ããŒã¯69åã®ã¬ã ããŒã«ãè²·ãããšãã§ããŸãã
åç: ####69
| 69
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ãããã·ã§ããã«ã¯çŸåšãç¬ã5å¹ãç«ã2å¹ãé³¥ã10矜ããŸããåºå
ã®ãããã®è¶³ã¯åèšã§äœæ¬ãããŸããïŒ
|
ç¬ã¯4æ¬ã®è¶³ãæã£ãŠããã®ã§ã5å¹ã®ç¬ã®è¶³ã®æ°ã¯:
5å¹ Ã 4æ¬ = 20æ¬
ç«ã¯4æ¬ã®è¶³ãæã£ãŠããã®ã§ã2å¹ã®ç«ã®è¶³ã®æ°ã¯:
2å¹ Ã 4æ¬ = 8æ¬
é³¥ã¯2æ¬ã®è¶³ãæã£ãŠããã®ã§ã10矜ã®é³¥ã®è¶³ã®æ°ã¯:
10矜 à 2æ¬ = 20æ¬
åºå
ã®ãããã®è¶³ã®åèšã¯:
20æ¬ (ç¬) + 8æ¬ (ç«) + 20æ¬ (é³¥) = 48æ¬
ãããã£ãŠãåºå
ã®ãããã®è¶³ã®åèšã¯48æ¬ã§ãã
åçïŒ####48
| 48
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ãžã£ããŒã«ã¯ãžã ã«ããŸãã圌ã¯8ãã³ãã®éãã䜿ã£ãŠããŸããã圌ã¯äœ¿çšããéãã50%å¢ãããŸãããããéãããããšãããã£ãã®ã§ã圌ã¯ãããã2ãã³ã軜ãéãã䜿ããŸãã圌ãä»äœ¿ã£ãŠããéãã¯äœãã³ãã§ããïŒ
|
ãžã£ããŒã«ã¯æåã«8ãã³ãã®éãã䜿ã£ãŠããŸãã
ãŸãã圌ã䜿çšããéãã50%å¢ãããšã次ã®ããã«èšç®ã§ããŸãïŒ
8ãã³ã à 50% = 8ãã³ã à 0.5 = 4ãã³ã
次ã«ã8ãã³ã + 4ãã³ã = 12ãã³ãã§ãã
ãããã圌ã¯12ãã³ãã®éããéãããããšãããããŸããã®ã§ã圌ã¯ãããã2ãã³ã軜ãéãã䜿ããŸãã
12ãã³ã - 2ãã³ã = 10ãã³ãã§ãã
ãããã£ãŠããžã£ããŒã«ãä»äœ¿ã£ãŠããéãã¯10ãã³ãã§ãã
çãã¯10ãã³ããã€ãŸãã####10ãã§ãã
| 10
|
é£è¡æ©ã¯3æéã§1200ãã€ã«ãé£ã³ãŸãããã®é床ã§ããã«2000ãã€ã«é£ã¶ã®ã«è¿œå ã§äœæéããããŸããïŒ
|
ãŸããé£è¡æ©ã®éåºŠãæ±ããŸãã3æéã§1200ãã€ã«é£ã¶ã®ã§ãéåºŠã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
é床 = è·é¢ ÷ æé = 1200ãã€ã« ÷ 3æé = 400ãã€ã«/æé
次ã«ã2000ãã€ã«ãé£ã¶ã®ã«ãããæéãèšç®ããŸãã
æé = è·é¢ ÷ é床 = 2000ãã€ã« ÷ 400ãã€ã«/æé = 5æé
ãããã£ãŠã2000ãã€ã«é£ã¶ã®ã«è¿œå ã§ãããæéã¯5æéã§ãã
åçã¯ã####5
| 5
|
æææ¥ã«ã¢ãŒã±ãŒãã§8ãã«äœ¿ã£ããã¯ãŒãã¯ãç«ææ¥ã«æææ¥ã®2åãæ°Žææ¥ã«ã¯ç«ææ¥ã®4åã®éé¡ãã¢ãŒã±ãŒãã§äœ¿ããŸããããšããš100ãã«æã£ãŠããå Žåã圌ã¯ãããæ®ããŠããŸããïŒ
|
ãã¯ãŒãã®æ¯åºãèšç®ããŠãããŸãã
1. **æææ¥ã®æ¯åº**: 8ãã«
2. **ç«ææ¥ã®æ¯åº**: æææ¥ã®2å
- ç«ææ¥ã®æ¯åº = 8ãã« Ã 2 = 16ãã«
3. **æ°Žææ¥ã®æ¯åº**: ç«ææ¥ã®4å
- æ°Žææ¥ã®æ¯åº = 16ãã« Ã 4 = 64ãã«
次ã«ããã¯ãŒãã®åèšæ¯åºãæ±ããŸãã
- åèšæ¯åº = æææ¥ã®æ¯åº + ç«ææ¥ã®æ¯åº + æ°Žææ¥ã®æ¯åº
- åèšæ¯åº = 8ãã« + 16ãã« + 64ãã« = 88ãã«
圌ã®åãã®éé¡ã¯100ãã«ãªã®ã§ãæ®ã£ãŠããéé¡ã¯æ¬¡ã®éãã§ãã
- æ®ãã®éé¡ = åãã®éé¡ - åèšæ¯åº
- æ®ãã®éé¡ = 100ãã« - 88ãã« = 12ãã«
ãããã£ãŠããã¯ãŒãã¯æ®ã12ãã«æã£ãŠããŸããåçã¯ä»¥äžã®éãã§ãã
#### 12
| 12
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