answer_number
int64 0
1k
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stringlengths 32
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97 |
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æ¥ææ¥ = åææ¥ã®å°æ° - 5 = 5 - 5 = 0å°
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- æææ¥ïŒ20å°
- ç«ææ¥ïŒ25å°
- æ°Žææ¥ïŒ22å°
- æšææ¥ïŒ10å°
- éææ¥ïŒ10å°
- åææ¥ïŒ5å°
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åèš = 20 + 25 + 22 + 10 + 10 + 5 + 0 = 92å°
\]
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#### 92
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\[
14 \text{æ¥} \times 9 \text{å/æ¥} = 126 \text{å}
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4 \text{å} \times 1.50 \text{ãã«/å} = 6.00 \text{ãã«}
\]
æ®ãã®é å€ã¯ã126åã®ãã¡4åãåŒãã122åã§ããæ®ãã®é å€ã¯ãããã5.50ãã«ããããŸãã®ã§ããã®122åã®åèšè²»çšã¯æ¬¡ã®ããã«èšç®ãããŸãã
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122 \text{å} \times 5.50 \text{ãã«/å} = 671.00 \text{ãã«}
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æåŸã«ããã³ãªãŒãé å€ã«ãããç·è²»çšã¯ã4åã®é å€ã®åèšãš122åã®é å€ã®åèšãè¶³ãããã®ã§ãã
\[
6.00 \text{ãã«} + 671.00 \text{ãã«} = 677.00 \text{ãã«}
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ãããã£ãŠããã³ãªãŒãé å€ã«åèšã§è²»ãããéé¡ã¯677.00ãã«ã§ãã
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####677.00
|
20 |
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|
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#### 20
|
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ããŒãã³ã®çšŒãã éé¡ïŒ
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35 \text{ å} \times 2 \text{ ãã«} = 70 \text{ ãã«}
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\[
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\[
210 \text{ ãã«} - 70 \text{ ãã«} = 140 \text{ ãã«}
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2 + 3 + 4 = 9 ãã«
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|
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#### 16
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- é± 0: 3 å (åã)
- é± 1: 3 + 2 = 5 å
- é± 2: 5 + 2 = 7 å
- é± 3: 7 + 2 = 9 å
- é± 4: 9 + 2 = 11 å
- é± 5: 11 + 2 = 13 å
ãããã£ãŠã5 é±éåŸã«ã¯ 13 åã®ãã®ããžã£ã°ãªã³ã°ã§ããããã«ãªããŸãã
åç: ####13
|
140 |
ãžã§ããµã¯ãããã 30 人ã®çåŸããã 3 ã€ã®å幎çã®ã¯ã©ã¹ãšã50 人ã®çåŸããã P.E. ã¯ã©ã¹ã®ããã«ã«ããã±ãŒããäœãå¿
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30人 à 3ã¯ã©ã¹ = 90人
次ã«ãP.E. ã¯ã©ã¹ã®çåŸæ°ã¯50人ã§ãã
次ã«ãå
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90人 (å幎çã®ã¯ã©ã¹) + 50人 (P.E. ã¯ã©ã¹) = 140人
ãžã§ããµã¯åèšã§140åã®ã«ããã±ãŒããäœãå¿
èŠããããŸãã
ãããã£ãŠãåç㯠#### 140 ã§ãã
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720 |
ãã£ãªãŒã¯æçµŠ 8 ãã«ã§é±ã« 35 æéåããŠããŸãã圌女ããã®ä»äºãå§ããŠãã 1 ã¶æãçµã¡ãŸããã圌女ã¯èªè»¢è»ã 400 ãã«ã§è³Œå
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æçµŠã¯ 8 ãã«ã§ãé±ã« 35 æéåããŠããŸãããïŒ
æã«åãæé = 35 æé/é± Ã 4 é± = 140 æé
æçµŠ = æçµŠ à æã«åãæé = 8 ãã« Ã 140 æé = 1120 ãã«
èªè»¢è»ã®è³Œå
¥äŸ¡æ Œã¯ 400 ãã«ã§ãã
ãããã£ãŠãèªè»¢è»ã賌å
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æ®ãã®ãé = æçµŠ - èªè»¢è»ã®äŸ¡æ Œ = 1120 ãã« - 400 ãã« = 720 ãã«
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¥ããåŸã720 ãã«æ®ããŸãã
åç㯠#### 720 ã§ãã
|
6 |
ã¹ãã©ãšãã¥ã€ã³ã¯ã«ã¯ã1人ãããæé250åã®ç³ãããã¯ãç©ã¿èŸŒãé床ã§ãç©èŒèœåã6000åã®ç³ãããã¯ã®ãã©ãã¯ãç©ã¿èŸŒãã§ããŸãã圌ãã¯4æéåããåŸãåãé床ã§äœæ¥ãã6人ã®ä»ã®äººã
ãå ãããŸããããã©ãã¯ãç©ã¿èŸŒãã®ã«äœæéããããŸãããïŒ
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æåã«ãã¹ãã©ãšãã¥ã€ã³ã¯ã«ã4æéåãããšãã«ç©ã¿èŸŒãã ç³ãããã¯ã®æ°ãèšç®ããŸãã圌ãã¯1人ãããæé250åã®é床ã§äœæ¥ãããŠããŸãã
2人ã§ã®æéã¯æ¬¡ã®ããã«èšç®ãããŸãïŒ
250å/æ à 2人 = 500å/æ
4æéåããã®ã§ã次ã®ããã«ç©ã¿èŸŒãã ç³ãããã¯ã®æ°ãèšç®ããŸãïŒ
500å/æ Ã 4æé = 2000å
次ã«ããã©ãã¯ã®ç©èŒèœåã¯6000åã®ç³ãããã¯ã§ãã®ã§ãæ®ãã®ç©ã¿èŸŒãå¿
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6000å - 2000å = 4000å
ãã§ã«2人ãåããŠ4æéçµã£ãæç¹ã§ãæ®ãã®äœæ¥ã«ã¯6人ãå ãããŸããããã§åèš8人ã«ãªããŸããã8人ãç©èŸŒãæéã¯æ¬¡ã®ããã«èšç®ãããŸãïŒ
250å/æ à 8人 = 2000å/æ
æ®ãã®4000åãç©ã¿èŸŒãã®ã«ãããæéã¯æ¬¡ã®ããã«èšç®ãããŸãïŒ
4000å ÷ 2000å/æ = 2æé
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4æé + 2æé = 6æé
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####6
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48 |
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å容èœå = 40è à 2人/è = 80人
æ€
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åã®æ°ã¯æ¬¡ã®ããã«èšç®ããŸãã
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å = 40è Ã (2/5) = 16è
䜿çšãããŠããæ€
å = 40è - 16è = 24è
䜿çšãããŠããæ€
åã«åº§ã£ãŠãã人æ°ã¯æ¬¡ã®ããã«èšç®ããŸãã
åºåžããŠããäººæ° = 䜿çšãããŠããæ€
åæ° à 2人/è = 24è à 2人/è = 48人
ãããã£ãŠãåç· åœ¹äŒã®äŒè°ã«åºåžããã¡ã³ããŒã®æ°ã¯48人ã§ãã
åç: ####48
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25 |
ãã«ã¯å庫ã¯ã48æ¬ã®çé
žæ°Žã1ã±ãŒã¹ã§12.00ãã«ã§è²©å£²ããŠããŸããå°å
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žæ°Žã®1æ¬ãããã®äŸ¡æ Œãèšç®ããŸãã
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1æ¬ãããã®äŸ¡æ Œã¯ \( \frac{12.00ãã«}{48æ¬} = 0.25ãã« \) ã§ãã
次ã«ãã¹ãŒããŒããŒã±ããã®çé
žæ°Žã®1æ¬ãããã®äŸ¡æ Œãèšç®ããŸãã
ã¹ãŒããŒããŒã±ããã§ã¯12æ¬ã§6.00ãã«ã§ãã®ã§ã
1æ¬ãããã®äŸ¡æ Œã¯ \( \frac{6.00ãã«}{12æ¬} = 0.50ãã« \) ã§ãã
ã¹ãŒããŒããŒã±ããã®äŸ¡æ Œããã«ã¯ååº«ã«æ¯ã¹ãŠã©ããããé«ãããæ±ããŸãã
ã¹ãŒããŒããŒã±ããã®1æ¬ãããã®äŸ¡æ Œã¯0.50ãã«ã§ããã«ã¯å庫ã®1æ¬ãããã®äŸ¡æ Œã¯0.25ãã«ã§ãããã
é«ããªãéé¡ã¯ \( 0.50ãã« - 0.25ãã« = 0.25ãã« \) ã§ãã
ãããã»ã³ãã«å€æãããšã1ãã«ã¯100ã»ã³ããªã®ã§ã
\( 0.25ãã« \times 100 = 25 \) ã»ã³ãã®å·®ã«ãªããŸãã
ãããã£ãŠãã¹ãŒããŒããŒã±ããã®ãã®ååŒã¯1æ¬ããã25ã»ã³ãé«ãã§ãã
åçã¯æ¬¡ã®éãã§ãïŒ ####25
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18 |
ãžã§ã€ã¯ç«ã®ããã¡ãçšã«ã€ãŒã³ã®çãå·»ããŠããŸããæåã®çã¯2çªç®ã®çã®ååã®å€§ããã§ãã3çªç®ã®çã¯æåã®çã®3åã®å€§ããã§ãã圌女ã¯3çªç®ã®çã«27ãã£ãŒãã®ã€ãŒã³ã䜿çšããŸããã圌女ã¯2çªç®ã®çã«äœãã£ãŒãã®ã€ãŒã³ã䜿çšããŸãããïŒ
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å ±ãæŽçããŸãã
1. 第1ã®çïŒ\( A \)ïŒã¯ç¬¬2ã®çïŒ\( B \)ïŒã®ååã®å€§ããã§ãã
2. 第3ã®çïŒ\( C \)ïŒã¯ç¬¬1ã®çã®3åã®å€§ããã§ãã
3. 第3ã®çã«ã¯27ãã£ãŒãã®ã€ãŒã³ã䜿çšãããŸããã
ãŸãã第3ã®çïŒ\( C \)ïŒã®å€§ãããæ°åŒã«ããŸãã
\( C = 27 \) ãã£ãŒãã
第1ã®çã第3ã®çã®å€§ããã®1/3ãªã®ã§ã
\( A = \frac{C}{3} = \frac{27}{3} = 9 \) ãã£ãŒãã
次ã«ã第2ã®çïŒ\( B \)ïŒã¯ç¬¬1ã®çã®2åã®å€§ãããªã®ã§ã
\( B = 2A = 2 \times 9 = 18 \) ãã£ãŒãã
ãããã£ãŠããžã§ã€ã¯ç¬¬2ã®çã«18ãã£ãŒãã®ã€ãŒã³ã䜿çšããŸããã
çãã¯æ¬¡ã®éãã§ãã
#### 18
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50 |
ãã€ãªãŒã¯æ¯å¹Ž 3 ã€ã³ããã€æé·ããŸããçŸåšã®åœŒå¥³ã®èº«é·ã 20 ã€ã³ãã§ããå Žåã10 幎åŸã®åœŒå¥³ã®èº«é·ã¯ããã€ã«ãªããŸããïŒ
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çŸåšã®èº«é·: 20 ã€ã³ã
幎éæé·: 3 ã€ã³ã
æé: 10 幎
10 幎åŸã®èº«é·ã¯æ¬¡ã®ããã«èšç®ããŸãã
10 幎åŸã®èº«é· = çŸåšã®èº«é· + (幎éæé· à 幎æ°)
10 幎åŸã®èº«é· = 20 ã€ã³ã + (3 ã€ã³ã à 10)
10 幎åŸã®èº«é· = 20 ã€ã³ã + 30 ã€ã³ã
10 幎åŸã®èº«é· = 50 ã€ã³ã
ãããã£ãŠããã€ãªãŒã®10幎åŸã®èº«é·ã¯ 50 ã€ã³ãã«ãªããŸãã
åç: ####50
|
25 |
ãã㯠10 人ã®ã«ãŒã ã¡ã€ããæã£ãŠããŸãããžã§ã³ã¯ããã® 2 åã®ã«ãŒã ã¡ã€ããã 5 人å€ãã®ã«ãŒã ã¡ã€ããæã£ãŠããŸãããžã§ã³ã¯äœäººã®ã«ãŒã ã¡ã€ããæã£ãŠããŸããïŒ
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ãã㯠10 人ã®ã«ãŒã ã¡ã€ããæã£ãŠããŸãããžã§ã³ã¯ããã® 2 åã®ã«ãŒã ã¡ã€ããã 5 人å€ãã®ã«ãŒã ã¡ã€ããæã£ãŠããã®ã§ããŸãããã®ã«ãŒã ã¡ã€ãã® 2 åãèšç®ããŸãã
ããã®ã«ãŒã ã¡ã€ãã®æ° = 10
ããã®ã«ãŒã ã¡ã€ãã® 2 å = 10 à 2 = 20
次ã«ããžã§ã³ã®ã«ãŒã ã¡ã€ãã®æ°ãæ±ããŸãïŒ
ãžã§ã³ã®ã«ãŒã ã¡ã€ãã®æ° = 20 + 5 = 25
ãããã£ãŠããžã§ã³ã¯ 25 人ã®ã«ãŒã ã¡ã€ããæã£ãŠããŸãã
æçµçãªåçã¯ã#### 25 ã§ãã
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æåã®ç«ã¯1åéã«3å鳎ããŸãïŒ
- æåã®ç«ã®é »åºŠ = 3å/å
2çªç®ã®ç«ã¯æåã®ç«ã®2åã®é »åºŠã§é³ŽããŸãïŒ
- 2çªç®ã®ç«ã®é »åºŠ = 3å/å à 2 = 6å/å
3çªç®ã®ç«ã¯2çªç®ã®ç«ã®1/3ã®é »åºŠã§é³ŽããŸãïŒ
- 3çªç®ã®ç«ã®é »åºŠ = 6å/å ÷ 3 = 2å/å
次ã«ã1å¹ã®ç«ã5åéã§é³Žãåæ°ãèšç®ããŸãïŒ
- æåã®ç«ïŒ3å/å à 5å = 15å
- 2çªç®ã®ç«ïŒ6å/å à 5å = 30å
- 3çªç®ã®ç«ïŒ2å/å à 5å = 10å
æåŸã«ã3å¹ã®ç«ã®åèšã®é³Žã声ã®åæ°ãèšç®ããŸãïŒ
15å + 30å + 10å = 55å
ãããã£ãŠã3å¹ã®ç«ã5åéã§åèšé³Žãåæ°ã¯55åã§ãã
åçïŒ####55
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- ãã³ã°ãµã€ãºããã2å°ã§ã2人 à 2å° = 4人ãå容ã§ããŸãã
- ãœãã¡ããã1å°ã§1人ãå容ã§ããŸãã
ãããã£ãŠã1éšå±ã§å容ã§ããçåŸã®ç·æ°ã¯:
4人 + 1人 = 5人ã§ãã
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å¿
èŠãªéšå±ã®æ° = 30人 ÷ 5人/éšå± = 6éšå±
ãããã£ãŠãæ ¡é·ã¯6éšå±ã®äºçŽãå¿
èŠã§ãã
åç㯠#### 6 ã§ãã
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販売ããã³ãŒã³ã®åæ° = 100ã㫠÷ 2ãã«/ã³ãŒã³ = 50ã³ãŒã³
次ã«ã圌ã¯6人ã«1人ã®ã客ããã«ç¡æã®ã¢ã€ã¹ã¯ãªãŒã ã³ãŒã³ãæäŸããŠããŸãããããã£ãŠãæäŸããç¡æã³ãŒã³ã®åæ°ã¯ã販売ããã³ãŒã³ã®åæ°ã6ã§å²ããŸãã
æäŸããç¡æã³ãŒã³ã®åæ° = 50ã³ãŒã³ ÷ 6 â 8.33
æŽæ°ã§èããå¿
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ãããã£ãŠãçãã¯ã####8ãã§ãã
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å人㫠40 åã®è²æ®»ããããã®ã§ãæ®ãã¯:
180 - 40 = 140 åã
次ã«ãå
åŒã« 30 åã®è²æ®»ããããã®ã§ãæ®ãã¯:
140 - 30 = 110 åã
æ®ãã®è²æ®»ã®ååã売ããšãæ®ãæ°ã¯:
110 ÷ 2 = 55 åã
ãããã£ãŠãã¢ãªã¯æçµçã« 55 åã®è²æ®»ãæã£ãŠããŸããã
#### 55
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500 |
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10ç« Ã 40ããŒãž/ç« = 400ããŒãž
次ã«ã圌女ã¯11ç« ç®ã®20ããŒãžãèªã¿ãŸããã
ãããã£ãŠããããã§ã«ãèªãã ããŒãžã®åèšã¯ã
400ããŒãžïŒ10ç« ïŒ + 20ããŒãžïŒ11ç« ç®ã®äžéšïŒ = 420ããŒãž
ãã®åŸã圌女ã¯11ç« ç®ã®æ®ãã®ããŒãžãèªã¿ãŸããã§ãããã2ç« ãèªã¿é²ããŸããã2ç« ã®ããŒãžæ°ã¯æ¬¡ã®ããã«èšç®ããŸãã
2ç« Ã 40ããŒãž/ç« = 80ããŒãž
ãããã£ãŠã圌女ãèªãã ããŒãžã®ç·æ°ã¯ã
420ããŒãž + 80ããŒãž = 500ããŒãž
æçµçã«ããããã§ã«ãåèšã§èªãã ããŒãžæ°ã¯500ããŒãžã§ããçãã¯ïŒ
#### 500
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110 |
ãžã§ãŒã ãºã¯ 4 ãã³ããã€ã®çèã®ããã¯ã 5 å賌å
¥ããŸãããçèã®äŸ¡æ Œã¯ 1 ãã³ãããã $5.50 ã§ãã圌ã¯åèšã§ãããæ¯æããŸãããïŒ
|
ãŸãããžã§ãŒã ãºã賌å
¥ããçèã®ããã¯ã®åèšééãèšç®ããŸãã
çèã®ããã¯ã¯ 5 åã1 ããã¯ããã 4 ãã³ãã§ããããåèšééã¯æ¬¡ã®ããã«ãªããŸãïŒ
\[
5 \text{ ããã¯} \times 4 \text{ ãã³ã/ããã¯} = 20 \text{ ãã³ã}
\]
次ã«ãçèã®äŸ¡æ Œã¯ 1 ãã³ãããã $5.50 ã§ãã®ã§ã20 ãã³ãã®çèã®åèšäŸ¡æ Œã¯æ¬¡ã®ããã«ãªããŸãïŒ
\[
20 \text{ ãã³ã} \times 5.50 \text{ãã«/ãã³ã} = 110 \text{ãã«}
\]
ãããã£ãŠããžã§ãŒã ãºã¯åèšã§ $110 æ¯æããŸãããçãã¯æ¬¡ã®ãšããã§ãïŒ
#### 110
|
9 |
ã¯ã©ã¹ã«ã¯ 40 人ã®çåŸãããŸããæ¬ åžããŠããçåŸã¯ 1/10 ã§ãåºåžããŠããçåŸã® 3/4 ãæå®€ã«ããŠãæ®ãã¯é£å ã«ããŸããé£å ã«ã¯äœäººã®çåŸãããŸããïŒ
|
ã¯ã©ã¹ã«ã¯ 40 人ã®çåŸãããã®ã§ãæ¬ åžããŠããçåŸã®äººæ°ãèšç®ããŸãã
æ¬ åžããŠããçåŸã®äººæ°ã¯:
\[
\frac{40}{10} = 4 \, \text{人}
\]
åºåžããŠããçåŸã®äººæ°ã¯:
\[
40 - 4 = 36 \, \text{人}
\]
åºåžããŠããçåŸã® 3/4 ãæå®€ã«ããã®ã§ãæå®€ã«ããçåŸã®äººæ°ãèšç®ããŸãã
æå®€ã«ããçåŸã®äººæ°ã¯:
\[
\frac{3}{4} \times 36 = 27 \, \text{人}
\]
ãããã£ãŠãé£å ã«ããçåŸã®äººæ°ã¯:
\[
36 - 27 = 9 \, \text{人}
\]
é£å ã«ã¯ 9 人ã®çåŸãããã®ã§ãæçµçãªåçã¯ïŒ
#### 9
|
74 |
倫婊ãšãã® 6 æ³ãš 10 æ³ã®åäŸ 2 人ãéåå°ã«è¡ãããšã«ããŸãããéåžžã®ãã±ãã㯠109 ãã«ã§ããã12 æ³æªæºã®åäŸã¯ 5 ãã«ã®å²åŒããããŸãã圌ããã«ãŠã³ã¿ãŒã« 500 ãã«ãæ¯æã£ãå Žåã圌ãã¯ãããã®ãé£ããåãåããŸããïŒ
|
倫婊ãšåäŸ2人ã®åèšäººæ°ã¯4人ã§ãã
倧人2人ãšåäŸ2人ã®ãã±ãã代ãèšç®ããŸãã
éåžžã®ãã±ããã¯109ãã«ã§ããã12æ³æªæºã®åäŸïŒ6æ³ãš10æ³ïŒã¯5ãã«ã®å²åŒãããã®ã§ãåäŸã®ãã±ããã¯æ¬¡ã®ããã«èšç®ããŸãïŒ
- 倧人2人ã®ãã±ãã代: 109ãã« Ã 2 = 218ãã«
- 6æ³ã®åäŸã®ãã±ãã代: 109ãã« - 5ãã« = 104ãã«
- 10æ³ã®åäŸã®ãã±ãã代: 109ãã« - 5ãã« = 104ãã«
ããããåèšããŸãïŒ
218ãã« (倧人) + 104ãã« (6æ³) + 104ãã« (10æ³) = 426ãã«
æ¯æã£ãéé¡ã¯500ãã«ãªã®ã§ããé£ãã¯æ¬¡ã®ããã«èšç®ããŸãïŒ
500ãã« - 426ãã« = 74ãã«
ãããã£ãŠã圌ãã¯ãããã®ãé£ããåãåããŸããïŒ
#### 74
|
20 |
ãã¬ã€ã³ã¯åç©ã®ãããã€åœ«å»ãäœããŸãã倧ããªåç©ã¯ 4 æ¬ã®ããããã䜿ããå°ããªåç©ã¯ 2 æ¬ã䜿ããŸãã圌女ã¯å€§ããªåç©ã® 3 åã®æ°ã®å°ããªåç©ãäœããå°ããªåç©ã«ã¯ 12 æ¬ã®ããããã䜿ããŸããããã¬ã€ã³ã¯ãã¹ãŠã®åç©ãäœãã®ã«åèšã§ããã€ã®ããããã䜿ããŸãããïŒ
|
ãã¬ã€ã³ãäœã倧ããªåç©ã®æ°ã \( x \) ãšããŸãããããšã圌女ã¯å°ããªåç©ã \( 3x \) äœããŸãã
å°ããªåç©ã«ã¯12æ¬ã®ããããã䜿ããã1å¹ã«ã€ã2æ¬ã®ããããã䜿ããããæ¬¡ã®ããã«èšç®ã§ããŸãã
å°ããªåç©ã®æ°ã¯ \( 3x \) ã§ãã®ã§ãå
šãŠã®å°ããªåç©ã«äœ¿ãããããããã®æ¬æ°ã¯ã
\[
2 \times 3x = 6x
\]
ãããŠã圌女ã¯å€§ããªåç©ãäœãããã«ã4æ¬ã®ããããã䜿ããããã \( x \) å¹ã§ããããã
\[
4x
\]
ãããã£ãŠããã¬ã€ã³ãå
šéšã®åç©ãäœãã®ã«äœ¿ã£ãããããã®åèšã¯ã
\[
6x + 4x = 10x
\]
å°ããªåç©ã«ã¯åèšã§12æ¬ã®ããããã䜿çšããããã
\[
6x = 12
\]
ãããã \( x \) ãæ±ããŸãã
\[
x = \frac{12}{6} = 2
\]
ãã£ãŠã倧ããªåç©ã¯ \( x = 2 \) å¹ããããŠå°ããªåç©ã¯ \( 3x = 3 \times 2 = 6 \) å¹ã€ãããŸãã
次ã«ããã¬ã€ã³ã䜿ãããããã®åèšæ°ãæ±ããŸãã
倧ããªåç©ã«äœ¿ãããããã¯
\[
4 \times 2 = 8
\]
å°ããªåç©ã«äœ¿ãããããã¯
\[
2 \times 6 = 12
\]
ãããã£ãŠãç·ããããæ°ã¯
\[
8 + 12 = 20
\]
ãã¬ã€ã³ããã¹ãŠã®åç©ãäœãã®ã«äœ¿ã£ãããããã®æ°ã¯ãæçµçã«20æ¬ã§ãã
çãã¯####20ã§ãã
|
6 |
3 ã€ã®å®¶æããããã 4 人ã§ã7 æ¥éã®äŒæãå
±æããŠããŸãã誰ãããæ°ãããã®ãæã«å
¥ããåã«ã1 æ¥ã« 1 æã®å€§ããªããŒãã¿ãªã«ã䜿çšããŸããæŽæ¿¯æ©ã¯ 1 ã€ã®ç©ã¿è·ã§ 14 æã®å€§ããªããŒãã¿ãªã«ãä¿æã§ããŸãããã¹ãŠã®å€§ããªããŒãã¿ãªã«ãæŽãã®ã«ãäœåã®æŽæ¿¯ãå¿
èŠã§ããïŒ
|
ãŸãã3ã€ã®å®¶æããããã4人ã§ãããããå
šäœã®äººæ°ã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
äººæ° = 3å®¶æ à 4人 = 12人
次ã«ãåäººãæ°ããããŒãã¿ãªã«ã䜿çšãããšä»®å®ãããšã7æ¥éã§å¿
èŠãªããŒãã¿ãªã«ã®ææ°ã¯æ¬¡ã®ããã«ãªããŸãã
å¿
èŠãªããŒãã¿ãªã«ææ° = äººæ° Ã æ¥æ° = 12人 à 7æ¥ = 84æ
æŽæ¿¯æ©ã¯1åã®ç©ã¿è·ã§14æã®ããŒãã¿ãªã«ãæŽããŸãã®ã§ãå¿
èŠãªæŽæ¿¯åæ°ã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
å¿
èŠãªæŽæ¿¯åæ° = å¿
èŠãªããŒãã¿ãªã«ææ° ÷ æŽæ¿¯æ©ã®å®¹é
å¿
èŠãªæŽæ¿¯åæ° = 84æ ÷ 14æ/å = 6å
ãããã£ãŠããã¹ãŠã®å€§ããªããŒãã¿ãªã«ãæŽãã®ã«å¿
èŠãªæŽæ¿¯ã®åæ°ã¯6åã§ãã
çãã¯6ã§ãã
#### 6
|
8 |
éåžžã1 ã¬ãã³ã®ããŒã«ãã«ã¯ã¯ $3 ã§ãããçŸåšã¯ $2 ã§è²©å£²ãããŠããŸãããŸãã1 ç®±ã®ã·ãªã¢ã«ã¯ $1 ã®å²åŒã§è²©å£²ãããŠããŸãã3 ã¬ãã³ã®ããŒã«ãã«ã¯ãš 5 ç®±ã®ã·ãªã¢ã«ã賌å
¥ããå Žåãå²åŒã«ãã£ãŠãããç¯çŽã§ããŸããïŒ
|
ãŸããéåžžã®äŸ¡æ Œã§ã®è³Œå
¥ã«ãããéé¡ãèšç®ããŸãã
1. **ããŒã«ãã«ã¯ã®éåžžäŸ¡æ Œ**:
- 1 ã¬ãã³ã®ããŒã«ãã«ã¯ã¯ $3 ã§ã3 ã¬ãã³ã賌å
¥ãããšã
\[
3 \, \text{ã¬ãã³} \times 3 \, \text{ãã«/ã¬ãã³} = 9 \, \text{ãã«}
\]
2. **ã·ãªã¢ã«ã®éåžžäŸ¡æ Œ**:
- 1 ç®±ã®ã·ãªã¢ã«ã®éåžžäŸ¡æ Œã $1 ãšãããšã5 ç®±ã®å Žåã¯ã
\[
5 \, \text{ç®±} \times 1 \, \text{ãã«/ç®±} = 5 \, \text{ãã«}
\]
ã€ãŸããéåžžã®åèšéé¡ã¯
\[
9 \, \text{ãã«} + 5 \, \text{ãã«} = 14 \, \text{ãã«}
\]
次ã«ãå²åŒåŸã®äŸ¡æ Œãèšç®ããŸãã
1. **ããŒã«ãã«ã¯ã®å²åŒäŸ¡æ Œ**:
- 1 ã¬ãã³ã®ããŒã«ãã«ã¯ã $2 ã®å Žåã3 ã¬ãã³ã®äŸ¡æ Œã¯ã
\[
3 \, \text{ã¬ãã³} \times 2 \, \text{ãã«/ã¬ãã³} = 6 \, \text{ãã«}
\]
2. **ã·ãªã¢ã«ã®å²åŒäŸ¡æ Œ**:
- ã·ãªã¢ã«ã $1 ã®å²åŒã§è²©å£²ãããŠããããã1 ç®±ã®äŸ¡æ Œã¯ $1 ã®å²åŒãé©çšããåŸã®äŸ¡æ Œãããªãã¡ $0 ã«ãªããŸãã
- ãããã£ãŠã5 ç®±ã®åèšè²»çšã¯ã
\[
5 \, \text{ç®±} \times 0 \, \text{ãã«/ç®±} = 0 \, \text{ãã«}
\]
ãããã£ãŠãå²åŒåŸã®åèšéé¡ã¯
\[
6 \, \text{ãã«} + 0 \, \text{ãã«} = 6 \, \text{ãã«}
\]
次ã«ãå²åŒã«ãã£ãŠç¯çŽã§ããéé¡ãèšç®ããŸãã
\[
\text{ç¯çŽé¡} = \text{éåžžäŸ¡æ Œ} - \text{å²åŒåŸäŸ¡æ Œ} = 14 \, \text{ãã«} - 6 \, \text{ãã«} = 8 \, \text{ãã«}
\]
çµè«ãšããŠãå²åŒã«ãã£ãŠç¯çŽã§ããéé¡ã¯ $8 ã§ãã
çãïŒ####8
|
24 |
ãžã£ãã¹ã®ãªãã£ã¹ã¯ 3 éã«ããããªãã£ã¹ã«è¡ãããã«ã¯ 3 éåã®é段ãäžããªããã°ãªããŸããã1 æ¥ã«ã圌女㯠3 éåã®é段ã 5 åäžãã3 éåã®é段ã 3 åäžããæ®ãã®æéã¯ãšã¬ããŒã¿ãŒã䜿ããŸãããžã£ãã¹ã¯ 1 æ¥ã«åèšã§äœéåã®é段ãäžãäžãããŸããïŒ
|
ãžã£ãã¹ã¯1æ¥ã«ä»¥äžã®ããã«é段ãäžãäžããŸãïŒ
- éæ®µãäžãïŒ3éåïŒ: 5å
- éæ®µãäžãïŒ3éåïŒ: 3å
ãŸããäžãéæ®µã®åèšãèšç®ããŸãïŒ
3é Ã 5å = 15é
次ã«ãäžãéæ®µã®åèšãèšç®ããŸãïŒ
3é Ã 3å = 9é
次ã«ã圌女ã1æ¥ã«äžãäžãããåèšã®éæ°ãèšç®ããŸãïŒ
äžãéæ° + äžãéæ° = 15é + 9é = 24é
ãããã£ãŠããžã£ãã¹ã¯1æ¥ã«åèšã§24éåã®é段ãäžãäžãããŸãã
åçã¯ã#### 24
|
148 |
ãã§ã«ã³ã¯Ræå®æ ç»ã«å
¥å Žããããã«IDã確èªããŠããŸãã圌女ã¯ãªããŒãµã€ã髿 ¡ã®120人ã®åäŸã®20%ããŠãšã¹ããµã€ã髿 ¡ã®90人ã®åäŸã®70%ãããŠã³ãã³ããã髿 ¡ã®50人ã®åäŸã®ååãæåŠããŸãããäœäººã®åäŸãæ ç»ã«å
¥å ŽããŸãããïŒ
|
ããããã®é«æ ¡ããæåŠãããåäŸã®æ°ãèšç®ããå
šäœã®åäŸã®æ°ãããã®åèšãåŒããŠæ ç»ã«å
¥å Žã§ãã人æ°ãæ±ããŸãã
1. ãªããŒãµã€ã髿 ¡ã®æåŠããã人æ°:
120人ã®20% = 120 à 0.2 = 24人
2. ãŠãšã¹ããµã€ã髿 ¡ã®æåŠããã人æ°:
90人ã®70% = 90 à 0.7 = 63人
3. ããŠã³ãã³ããã髿 ¡ã®æåŠããã人æ°:
50人ã®50% = 50 à 0.5 = 25人
次ã«ãå
šäœã®æåŠããã人æ°ãåèšããŸãã
æåŠãããåèš = 24 + 63 + 25 = 112人
髿 ¡ã®åäŸã®ç·äººæ°ãèšç®ããŸãã
ç·äººæ° = 120 + 90 + 50 = 260人
æ ç»ã«å
¥å Žã§ããåäŸã®äººæ°ã¯ãç·äººæ°ããæåŠããã人æ°ãåŒããŸãã
å
¥å Žã§ããäººæ° = 260 - 112 = 148人
ãããã£ãŠãæ ç»ã«å
¥å ŽããåäŸã®æ°ã¯148人ã§ãã
åç: 148 ####
|
72 |
ã©ãªãŒã¯1æ¥ã«2åã30åãã€ç¬ã®æ£æ©ãšéã³ãããŸãããŸãã1æ¥ã«1/5æéãç¬ã®é€ããã«è²»ãããŸããã©ãªãŒã¯1æ¥ã«ç¬ã«ã©ããããã®æéãè²»ãããŠããŸããïŒ
|
ã©ãªãŒãç¬ã«è²»ããæéã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
1æ¥ã«ç¬ã®æ£æ©ãšéã³ã«è²»ããæéã¯ã2åã®30åãã€ãªã®ã§ïŒ
30å Ã 2 = 60å = 1æé
ããã«ãé€ããã«1/5æéãè²»ãããŠããŸãã
次ã«ãç¬ã«è²»ããæéãåèšããŸãïŒ
1æé + 1/5æé
1æéã¯5/5æéã«æç®ã§ããã®ã§ïŒ
5/5 + 1/5 = 6/5æé
6/5æéã¯ã1æéãš1/5æéïŒã€ãŸã12åïŒã§ãã
ãããã£ãŠãã©ãªãŒãç¬ã«è²»ããæéã¯1æéãš12åã§ãã
æçµçãªæéãæéåäœã§è¡šããšã
6/5æé = 1.2æé
ãããã£ãŠãã©ãªãŒã¯1æ¥ã«ç¬ã«è²»ããæéã¯1.2æéã§ãã
çãã¯ïŒ
#### 1.2
|
30 |
äžã€ã®æ¶æ¯ã¹ãã¬ãŒã¯çްèã®50%ãæ®ºããããäžã€ã®ã¹ãã¬ãŒã¯çްèã®25%ãæ®ºããŸãããããã圌ããæ®ºã现èã®ãã¡5%ã¯åããã®ã§ããäž¡æ¹ã®æ¶æ¯ã¹ãã¬ãŒãäžç·ã«äœ¿çšããå Žåãã©ã®ãããã®å²åã®çްèãæ®ããŸããïŒ
|
ãŸããæ¶æ¯ã¹ãã¬ãŒAã¯çްèã®50%ãæ®ºããæ¶æ¯ã¹ãã¬ãŒBã¯çްèã®25%ãæ®ºããŸããããããã®ã¹ãã¬ãŒã殺ã现èã®äžã§ã5%ã¯åããã®ã§ãããã®ãããéè€ãèæ
®ã«å
¥ããŠèšç®ããŸãã
1. ã¹ãã¬ãŒAã§æ®ºããã现è: 50%
2. ã¹ãã¬ãŒBã§æ®ºããã现è: 25%
3. äºã€ã®ã¹ãã¬ãŒãå
±éããŠæ®ºãã现è: 5%
éè€ãå«ããŠèšç®ããŸãã
ã¹ãã¬ãŒAãšBã®äž¡æ¹ã§æ®ºããã现èã®å²åã¯ã次ã®ããã«ãªããŸãã
ã¹ãã¬ãŒAãŸãã¯Bã§æ®ºã现èã®å²å = ã¹ãã¬ãŒAãæ®ºãå²å + ã¹ãã¬ãŒBãæ®ºãå²å - å
±éããŠæ®ºãå²å
ãããé©çšãããšæ¬¡ã®ããã«ãªããŸãïŒ
\[
50\% + 25\% - 5\% = 70\%
\]
ã€ãŸããäž¡æ¹ã®ã¹ãã¬ãŒã䜿çšããå Žåã70%ã®çްèãæ»ã«ãŸãã
ãããã£ãŠãæ®ã现èã®å²åã¯æ¬¡ã®ããã«ãªããŸãïŒ
\[
100\% - 70\% = 30\%
\]
åŸã£ãŠãæ®ã现èã®å²åã¯30%ã§ãã
æçµçãªåçã¯ã现èã®æ®ãã®å²åã¯30%ã§ãã®ã§ããããæ°åã§è¡šããšã####30ããšãªããŸãã
|
45 |
ãããŒã¯å°å
ã®æ± ã«ããééãæ°ããŠããŸãã圌ã¯ãééã®ãã¡è¡šé¢ã«ããã®ã¯ 25% ã§ãæ®ãã®ééã¯è¡šé¢äžãæ·±ãããŠèŠããªãããšãç¥ã£ãŠããŸãã圌ã 15 å¹ã®ééãæ°ããå Žåãã©ãã ãã®ééã衚é¢äžã«ããã§ããããïŒ
|
ãããŒãæ°ããéé㯠15 å¹ã§ãããã®ãã¡ã衚é¢ã«ããéé㯠25% ã§ãããã衚é¢ã«ããééã®æ°ãèšç®ããŸãã
衚é¢ã«ããééã®æ° = 15 å¹ Ã 25% = 15 å¹ Ã 0.25 = 3.75 å¹
ééã®æ°ã¯æŽæ°ã§ãããããå®éã«ã¯ 4 å¹ã®ééã衚é¢ã«ãããšèããŸãïŒå°æ°ãåãäžããŸãïŒã
次ã«ãå
šäœã®ééã®æ°ããã衚é¢ã«ããééã®æ°ãåŒãããšã§ã衚é¢äžã«ããééã®æ°ãæ±ããŸãã
å
šäœã®ééã®æ° = 衚é¢ã«ããééã®æ° ÷ 0.25 = 4 å¹ Ã· 0.25 = 16 å¹
衚é¢äžã«ããééã®æ° = å
šäœã®ééã®æ° - 衚é¢ã«ããééã®æ°
= 16 å¹ - 4 å¹ = 12 å¹
ãããã£ãŠããããŒã®æ± ã®ééã®ãã¡è¡šé¢äžã«ããéé㯠12 å¹ã§ãã
åçã¯ä»¥äžãšãªããŸãïŒ
#### 12
|
8 |
ãã«ã³æçåºã®ãªãŒããŒã¯ãè¿ã
ã®ç¥ç¥ã®ããã«äŒçµ±çãªæçãæºåããããšèãã3人ã®ç°ãªãèå±ãã4ãã³ãããã±ãŒãžã®çã²ãèãæ³šæããŸãããç¿æãæåã®èå±ã10ããã±ãŒãžãå±ããŸããããã®åŸã2æéã»ã©ããŠã2çªç®ã®èå±ãã7ããã±ãŒãžãå±ããŸãããæåŸã«ã倿®ãæã«3çªç®ã®èå±ã®é
éãå°çããŸããã3人ã®èå±ãå±ããçã²ãèã®ç·ééã¯100ãã³ãã§ããã3çªç®ã®èå±ã¯äœããã±ãŒãžãå±ããŸãããïŒ
|
æåã®èå±ãå±ããããã±ãŒãžã¯10ããã±ãŒãžã§ãåããã±ãŒãžã¯4ãã³ãã§ãã®ã§ãæåã®èå±ãå±ããçã²ãèã®ç·ééã¯ä»¥äžã®éãã§ãã
10ããã±ãŒãž à 4ãã³ã/ããã±ãŒãž = 40ãã³ã
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= 23 + 16
= 39 å
ãã®ããŒãºã 3 çåããŸãã®ã§ãåéšåã«ã¯ã39 ÷ 3 = 13 åã®ããŒãºãå
¥ããŸãã
次ã«ãåéšåããããŒãºãåãé€ãéã x ãšããŸããåãé€ããåŸã®ããŒãºã¯ã13 - x åã§ãããã®æ®ãã®ããŒãºã 2 åããŠã6 åã®ããŒãºãæããããšããŸãã
ãã®ãããæ¬¡ã®åŒãæãç«ã¡ãŸãã
2 * (13 - x) = 6
ãã®æ¹çšåŒãè§£ããŸãã
2 * (13 - x) = 6
26 - 2x = 6
26 - 6 = 2x
20 = 2x
x = 10
ãããã£ãŠãåéšåããåãé€ãããããŒãºã®æ°ã¯ 10 åã§ãã
æçµçãªåçã¯ã####10ã§ãã
|
6 |
ãžã§ããŒã 㯠150 ãã€ã«ã®èªè»¢è»æ
è¡ãããŠããŸãã圌㯠12 æ¥éãæ¯æ¥ 12 ãã€ã«ãã€èµ°ããããšèããŠããŸãã圌㯠13 æ¥ç®ã«ã©ãã ãèµ°ãã°ç®æšãéæã§ããŸããïŒ
|
ãžã§ããŒã ã¯æ¯æ¥ 12 ãã€ã«ã〠12 æ¥éèªè»¢è»ãèµ°ãèšç»ãããŠããŸãã
1. 圌ã12æ¥éã§èµ°ããã€ã«æ°ãèšç®ããŸãã
\[
12 \, \text{ãã€ã«/æ¥} \times 12 \, \text{æ¥} = 144 \, \text{ãã€ã«}
\]
2. ç®æšã®150ãã€ã«ã«å¯ŸããŠ144ãã€ã«ãèµ°ãã®ã§ãæ®ãã®ãã€ã«æ°ã¯ä»¥äžã®ããã«èšç®ããŸãã
\[
150 \, \text{ãã€ã«} - 144 \, \text{ãã€ã«} = 6 \, \text{ãã€ã«}
\]
ãããã£ãŠããžã§ããŒã ã¯13æ¥ç®ã«6ãã€ã«èµ°ãã°ç®æšãéæã§ããŸãã
çãã¯ã####6ãã§ãã
|
27 |
ããªãªã®ç髪åºã§ã¯ã鱿«ã¯ã«ãã代ã 50% é«ããªããŸããããªãªã¯æåŸã®ã«ãããæææ¥ã« 18 ãã«ã§æ¯æããŸãããããã§ã¯ã忥ã«ã¯ãããæ¯æã£ãããšã«ãªããŸããïŒ
|
ããªãªã®ç髪åºã§ã®ã«ãã代ã鱿«ã«50%é«ããªããšããããšã¯ã鱿«ã®ã«ãã代ã¯éåžžã®1.5åã«ãªããšããããšã§ãã
æææ¥ã«æ¯æã£ãã«ãã代18ãã«ã¯éåžžæéã§ãã®ã§ã鱿«ã«ã«ãããåããå Žåã®æéã¯æ¬¡ã®ããã«ãªããŸãïŒ
\[
\text{鱿«ã®ã«ãã代} = \text{éåžžã®ã«ãã代} \times 1.5
\]
ãããã£ãŠãéåžžã®ã«ãã代ã¯18ãã«ã§ãã
鱿«ã«åããã«ãã代ã¯ïŒ
\[
\text{鱿«ã®ã«ãã代} = 18 \times 1.5 = 27 \text{ãã«}
\]
ã€ãŸãã忥ã€ãŸãæ¥ææ¥ã«ã¯27ãã«ãæ¯æã£ãããšã«ãªããŸãã
ãããã£ãŠãçãã¯ïŒ
#### 27
|
295 |
ãžã§ã³ã¯ãããã¯ããŒãã£ãŒãéå¬ãããã®è²»çšãä»ã®3人ãšåãåããŸãã圌ã㯠1ãã³ãããã3ãã«ã®ãã³ããŒã¬ãŒã100ãã³ã賌å
¥ããèª¿å³æãšãããã³ã䜿ã£ãŠèª¿çããããã«80ãã«ãæ¯æããŸãããžã§ã³ã¯ã¢ã«ã³ãŒã«ãå
šãŠè³Œå
¥ãããã®è²»çšã¯200ãã«ã§ãããžã§ã³ã¯åèšã§ãããæ¯æããŸãããïŒ
|
ãŸãããããã¯ããŒãã£ãŒã®ç·è²»çšãèšç®ããŸãã
ãã³ããŒã¬ãŒã®è²»çš:
ãã³ããŒã¬ãŒã¯100ãã³ãã§ã1ãã³ãããã3ãã«ã§ãã
ãããã£ãŠããã³ããŒã¬ãŒã®ç·ã³ã¹ãã¯:
100ãã³ã à 3ãã«/ãã³ã = 300ãã«
èª¿å³æãšãããã³ã®ã³ã¹ã:
èª¿å³æãšãããã³ã®è²»çšã¯80ãã«ã§ãã
ã¢ã«ã³ãŒã«ã®ã³ã¹ã:
ãžã§ã³ãæ¯æã£ãã¢ã«ã³ãŒã«ã®è²»çšã¯200ãã«ã§ãã
ããããã¹ãŠã®è²»çšãåèšãããš:
300ãã« (ãã³ããŒã¬ãŒ) + 80ãã« (èª¿å³æãšãããã³) + 200ãã« (ã¢ã«ã³ãŒã«) = 580ãã«
次ã«ããžã§ã³ã¯ãã®åèšãä»ã®3人ãšåãåããŸããã圌ãã¢ã«ã³ãŒã«ãå
šãŠæ¯æã£ããããåœŒãæ¯æã£ãç·é¡ã¯580ãã«ã«ãªããŸãããããã£ãŠãæçµçã«ãžã§ã³ãæ¯æã£ãéé¡ã¯580ãã«ã§ãã
åŸã£ãŠããžã§ã³ãåèšã§æ¯æã£ãéé¡ã¯
#### 580
|
4 |
çºã®å¹Žéäºç®ã¯åèšã§ 32 åãã«ã§ããäºç®ã®ååãèŠå¯ã«å
ãŠããã12 åãã«ãæè²ã«å
ãŠãããŸããå
Œ
±ã¹ããŒã¹ã®ç®¡çã«ã¯ãããã®ãéãæ®ããŸããïŒ
|
çºã®å¹Žéäºç®ã¯ 32 åãã«ã§ããäºç®ã®ååãèŠå¯ã«å
ãŠãããã®ã§ãèŠå¯ã«å
ãŠãããéé¡ã¯ïŒ
32 åã㫠÷ 2 = 16 åãã«
次ã«ãæè²ã«å
ãŠãããéé¡ã 12 åãã«ã§ãã
ãããèæ
®ããŠãèŠå¯ãšæè²ã«å
ãŠãããéé¡ã®åèšã¯ïŒ
16 åãã« + 12 åãã« = 28 åãã«
æ®ãã®éé¡ãèšç®ããããã«ã幎éäºç®ããèŠå¯ãšæè²ã«å
ãŠãããåèšéé¡ãåŒããŸãïŒ
32 åãã« - 28 åãã« = 4 åãã«
ãããã£ãŠãå
Œ
±ã¹ããŒã¹ã®ç®¡çã«ã¯ 4 åãã«ãæ®ããŸãã
çã㯠4 ã§ãããããã£ãŠãæçµçãªåçã¯ïŒ
#### 4
|
72 |
ãžã§ãŒã ãºã¯ãµãã«ãŒããŒã ã«å
¥å£ããã¹ã¿ãŒéžæãšãªããŸãã圌ã¯è©Šåããšã« 4 ã€ã®ã¿ããããŠã³ã決ããããããã®ã¿ããããŠã³ã¯ 6 ç¹ã«çžåœããŸããã·ãŒãºã³ã¯ 15 詊åãããŸãããŸããã·ãŒãºã³äžã« 2 ç¹ã³ã³ããŒãžã§ã³ã 6 åæåãããŸããéå»ã®èšé²ã¯ã·ãŒãºã³äžã« 300 ç¹ã§ããããžã§ãŒã ãºã¯éå»ã®èšé²ãäœç¹äžåããŸãããïŒ
|
ãžã§ãŒã ãºã®ã·ãŒãºã³äžã«ç²åŸããç¹æ°ãèšç®ããŸãã
1. ã¿ããããŠã³ã®åŸç¹:
- 詊åããšã«4ã€ã®ã¿ããããŠã³ã決ããã®ã§ã15詊åã§ã¯:
\[
4 \, \text{ã¿ããããŠã³/詊å} \times 15 \, \text{詊å} = 60 \, \text{ã¿ããããŠã³}
\]
- ã¿ããããŠã³1ã€ã®ç¹æ°ã¯6ç¹ãªã®ã§ãåèšã®åŸç¹ã¯:
\[
60 \, \text{ã¿ããããŠã³} \times 6 \, \text{ç¹/ã¿ããããŠã³} = 360 \, \text{ç¹}
\]
2. ã³ã³ããŒãžã§ã³ã®åŸç¹:
- 2ç¹ã³ã³ããŒãžã§ã³ã6åæåãããã®ã§ãã³ã³ããŒãžã§ã³ããã®åŸç¹ã¯:
\[
6 \, \text{å} \times 2 \, \text{ç¹/å} = 12 \, \text{ç¹}
\]
3. åèšåŸç¹ãèšç®:
\[
360 \, \text{ç¹ïŒã¿ããããŠã³ïŒ} + 12 \, \text{ç¹ïŒã³ã³ããŒãžã§ã³ïŒ} = 372 \, \text{ç¹}
\]
4. éå»ã®èšé²(300ç¹)ãšã®å·®ãèšç®:
\[
372 \, \text{ç¹} - 300 \, \text{ç¹} = 72 \, \text{ç¹}
\]
ãããã£ãŠããžã§ãŒã ãºã¯éå»ã®èšé²ã72ç¹äžåããŸããã
åç: ####72
|
32 |
æææ¥ã«ãããã£ã¯ 30 æã®éçã«ãŒããæã£ãŠããŸããç«ææ¥ã«ã¯ãã®ååã倱ããŸããæ°Žææ¥ã«ã¯ 12 æã®éçã«ãŒãã賌å
¥ããŸããæšææ¥ã«ã¯ç«ææ¥ã«æã£ãŠããæ°ã® 1/3 ã賌å
¥ããŸããæšææ¥ã«ãããã£ã¯äœæã®éçã«ãŒããæã£ãŠããŸããïŒ
|
æææ¥ã«ãããã£ã¯30æã®éçã«ãŒããæã£ãŠããŸãã
ç«ææ¥ã«ã¯ãã®ååã倱ããŸãã®ã§ã
ç«ææ¥ã®ã«ãŒãã®ææ° = 30 ÷ 2 = 15æ
æ°Žææ¥ã«ã¯12æã®éçã«ãŒãã賌å
¥ããŸãã®ã§ã
æ°Žææ¥ã®ã«ãŒãã®ææ° = 15 + 12 = 27æ
æšææ¥ã«ã¯ç«ææ¥ã«æã£ãŠããæ°ã®1/3ã賌å
¥ããŸãã
æšææ¥ã«è³Œå
¥ããã«ãŒã = 15 ÷ 3 = 5æ
æšææ¥ã®ã«ãŒãã®ææ° = 27 + 5 = 32æ
ãããã£ãŠãæšææ¥ã«ãããã£ã¯32æã®éçã«ãŒããæã£ãŠããŸãã
åç㯠####32 ã§ãã
|
6 |
ãããã¯ã¹ã¯èгå
ãã¹ã®é転æã§ãã圌ã¯ç®çå°ãŸã§ 55 ãã€ã«ãé転ããç®çå°ããåºçºå°ç¹ã«æ»ãéã«ã¯ 10 ãã€ã«é·ãå¥ã®éãé転ããŸãã圌㯠1 ãã€ã«ã 2 åã§é転ã§ããç®çå°ã§ 2 æéæ»åšããŸããé転æãå
šè¡çšãå®äºããã®ã«äœæéããããŸããïŒ
|
ãããã¯ã¹ãå
šè¡çšãå®äºããã®ã«ãããæéãèšç®ããŸãã
1. **åºçºå°ç¹ããç®çå°ãŸã§ã®é転**:
- è·é¢: 55ãã€ã«
- é床: 1ãã€ã«ã2åã§
- æèŠæé: 55ãã€ã« à 2å/ãã€ã« = 110å
2. **ç®çå°ããåºçºå°ç¹ã«æ»ãéã®é転**:
- è·é¢: 55ãã€ã« + 10ãã€ã« = 65ãã€ã«
- æèŠæé: 65ãã€ã« à 2å/ãã€ã« = 130å
3. **ç®çå°ã§ã®æ»åšæé**:
- æ»åšæé: 2æé = 120å
4. **å
šå·¥çšã®æé**:
- åºçºå°ç¹ããç®çå°ãŸã§ã®é転æé: 110å
- ç®çå°ã§ã®æ»åšæé: 120å
- åºçºå°ç¹ã«æ»ããŸã§ã®é転æé: 130å
åèšæé = 110å + 120å + 130å = 360å
5. **æéã«å€æ**:
- 360å ÷ 60 = 6æé
ãããã£ãŠããããã¯ã¹ãå
šè¡çšãå®äºããã®ã«ãããæéã¯6æéã§ãã
æçµçãªåçã¯ä»¥äžã®éãã§ãïŒ
#### 6
|
9 |
ç¥ç¶ã®ã«ãŒã¯ããŒã«ããŒã¯ãã£ã³ãã«ã§æ ç»ã芳ãã®ã奜ãã§ãããã§äžæ ãããæ ç»ã¯ãã¹ãŠ 90 åéã§ããç«ææ¥ã«ã¯ããŒã«ããŒã¯ãã£ã³ãã«ã§ããã€ãã®ãã«ã¬ã³ã°ã¹ã®æ ç»ãåèšã§ 4 æé 30 å芳ãŸããããããŠæ°Žææ¥ã«ã¯ç«ææ¥ãšåããã£ã³ãã«ã§ç«ææ¥ã® 2 åã®æ ç»ã芳ãŸãããã«ãŒã¯ãããã® 2 æ¥éã§æå€§ã§äœæ¬ã®ãã«ã¬ã³ã°ã¹ã®æ ç»ã芳ãããšãã§ããŸãããïŒ
|
ãŸããç«ææ¥ã«ã«ãŒã芳ãåèšæéãåã«å€æããŸãã
4æé30åã¯ã4 à 60 + 30 = 240 + 30 = 270åã§ãã
次ã«ã1æ¬ã®æ ç»ã®é·ãã¯90åãªã®ã§ãç«ææ¥ã«èŠ³ãæ ç»ã®æ¬æ°ãèšç®ããŸãã
270å ÷ 90å/æ¬ = 3æ¬
ç«ææ¥ã«åç»ã3æ¬èгãã®ã§ãæ°Žææ¥ã«ã¯ç«ææ¥ã®2åã®æ ç»ã芳ãŸãã
3æ¬ Ã 2 = 6æ¬
ãããã£ãŠãç«ææ¥ãšæ°Žææ¥ã§èŠ³ãæ ç»ã®æ¬æ°ãåèšãããšã
3æ¬ïŒç«ææ¥ïŒ + 6æ¬ïŒæ°Žææ¥ïŒ = 9æ¬
ã«ãŒã¯ãããã®2æ¥éã§æå€§ã§9æ¬ã®ãã«ã¬ã³ã°ã¹ã®æ ç»ã芳ãããšãã§ããŸããã
ãããã£ãŠãæçµçãªåçã¯ã####9ãã§ãã
|
54 |
ã·ã«ãã¢ã®ããŒã«ãªãŒã¯ã50ãã«ä»¥äžã®äºå泚æã«å¯ŸããŠ10%ã®å²åŒãæäŸããŠããŸãã圌女ã¯15ãã«ãã€ã®2ã€ã®ããã·ã¥ãå3ãã«ã®6ã€ã®ã¯ãã¯ããµã³ããããŠå2ãã«ã®6ã€ã®ãã¿ãŒãã«ã¯ãã¹ã±ãããæ³šæããŸããå²åŒãé©çšããåŸãåœŒå¥³ã®æ³šæã¯ãããã«ãªããŸããïŒ
|
ãŸããã·ã«ãã¢ã®æ³šæã®åèšéé¡ãèšç®ããŸãã
1. **ããã·ã¥**: 15ãã« Ã 2 = 30ãã«
2. **ã¯ãã¯ããµã³**: 3ãã« Ã 6 = 18ãã«
3. **ãã¿ãŒãã«ã¯ãã¹ã±ãã**: 2ãã« Ã 6 = 12ãã«
次ã«ããããã®åèšãèšç®ããŸãã
åèšéé¡ = ããã·ã¥ + ã¯ãã¯ããµã³ + ãã¿ãŒãã«ã¯ãã¹ã±ãã
åèšéé¡ = 30ãã« + 18ãã« + 12ãã« = 60ãã«
ã·ã«ãã¢ã®æ³šæéé¡ã¯60ãã«ã§ãã50ãã«ä»¥äžã®äºå泚æã«10%ã®å²åŒãé©çšãããŸãã
å²åŒé¡ãèšç®ããŸãïŒ
å²åŒé¡ = 60ãã« Ã 0.10 = 6ãã«
å²åŒåŸã®åèšéé¡ãèšç®ããŸãïŒ
å²åŒåŸã®åèšéé¡ = 60ãã« - 6ãã« = 54ãã«
ãããã£ãŠãã·ã«ãã¢ã®æ³šæã¯ãããã«ãªãããšãããšã54ãã«ã«ãªããŸãã
åç: ####54
|
216 |
ããªã¹ã®ãªã«ãŒã·ã§ãã㯠6 ãæããšã« 90 ããã°ã©ã ã®ã¶ã©ãã䜿çšããŠããŸãã圌ã¯çç£éã 20 ããŒã»ã³ãå¢ããããšãèããŠããŸããçç£éãå¢ãããåŸã圌㯠1 幎éã§äœããã°ã©ã ã®ã¶ã©ããå¿
èŠã«ãªããŸããïŒ
|
ããªã¹ã¯6ãæããšã«90ããã°ã©ã ã®ã¶ã©ãã䜿çšããŠããã®ã§ã1幎éã§ã¯2åã®6ãæããããŸãããããã£ãŠã1幎éã§ã®ã¶ã©ãã®äœ¿çšéã¯æ¬¡ã®ããã«èšç®ã§ããŸãïŒ
1幎éã®äœ¿çšé = 90ããã°ã©ã à 2 = 180ããã°ã©ã
次ã«ãçç£éã20ããŒã»ã³ãå¢ãããšãå¿
èŠãªã¶ã©ãã®éã¯æ¬¡ã®ããã«èšç®ã§ããŸãïŒ
å¢å åŸã®çç£é = çŸåšã®çç£é à (1 + å¢å ç)
å¢å çã¯20ããŒã»ã³ããããªãã¡0.20ã§ãã
å¢å åŸã®å¿
èŠé = 180ããã°ã©ã à (1 + 0.20) = 180ããã°ã©ã à 1.20 = 216ããã°ã©ã
ãããã£ãŠã圌ã¯1幎éã§216ããã°ã©ã ã®ã¶ã©ããå¿
èŠã«ãªããŸãã
æçµçãªçãã¯ä»¥äžã®éãã§ãïŒ
#### 216
|
21 |
ã¡ã«ã¯ãã£ãµãªã³ãã3æ³å¹Žäžã§ãããã£ãµãªã³ãäºååæ³ã®ãšããã¡ã«ã¯äœæ³ã«ãªããŸããïŒ
|
ãã£ãµãªã³ã24æ³ã®ãšããã¡ã«ã¯ãã£ãµãªã³ãã3æ³å¹Žäžã§ãããããã¡ã«ã®å¹Žéœ¢ã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
ã¡ã«ã®å¹Žéœ¢ = ãã£ãµãªã³ã®å¹Žéœ¢ - 3æ³
ã¡ã«ã®å¹Žéœ¢ = 24æ³ - 3æ³ = 21æ³
ãããã£ãŠããã£ãµãªã³ã24æ³ã®ãšããã¡ã«ã¯21æ³ã«ãªããŸãã
åçïŒ####21
|
24 |
ãžã§ãŒã ãºã¯åœŒã® 2 æ¬ã®æšãããã¹ãŠã®æç©ãéããŸããããããã®æšã«ã¯ 20 æ¬ã®æ€ç©ããããŸãã忀ç©ã«ã¯ 1 ã€ã®çš®ãããã圌ã¯ãããã® 60% ãæ€ããŸãã圌ã¯äœæ¬ã®æšãæ€ããŸãããïŒ
|
ãŸãããžã§ãŒã ãºãæã£ãŠããæšã®æ¬æ°ã¯2æ¬ã§ãããããã®æšã«ã¯20æ¬ã®æ€ç©ããããŸãããããã£ãŠãå
šäœã®æ€ç©ã®æ¬æ°ã¯æ¬¡ã®ããã«èšç®ã§ããŸãã
2æ¬ã®æš à 20æ¬ã®æ€ç© = 40æ¬ã®æ€ç©
次ã«ã圌ã¯ãããã®æ€ç©ã®60%ãæ€ããŸãããããèšç®ãããšã
40æ¬ã®æ€ç© à 60% = 40 à 0.6 = 24æ¬ã®æ€ç©
ãããã£ãŠã圌ã¯24æ¬ã®æ€ç©ãæ€ããŸããããæšã®æ¬æ°ã§ã¯ãªããæ€ç©ã®æ¬æ°ã®ã¿ãèšç®ããŠããŸãã
åé¡ã¯ãäœæ¬ã®æšãæ€ããŸãããïŒããšãããŸãããäžããããæ
å ±ããã¯æšã®æ¬æ°ãçŽæ¥æ±ããããšã¯ã§ããŸããããã¹ãŠã®æ€ç©ã1ã€ã®æšããæ¥ãŠããããã§ã¯ãªãã®ã§ãæ€ããæ€ç©ã®æ¬æ°ãããæ€ããæšã®æ¬æ°ãçŽæ¥ç¥ãæ¹æ³ã¯ãããŸããã
æçµçãªçãã¯ãåœŒãæ€ããæšã®æ°ãæ±ããæ
å ±ãäžè¶³ããŠãããããç¹å®ã®æšã®æ¬æ°ã瀺ãããšã¯ã§ããŸããããæ€ããæ€ç©ã®æ°ã¯24æ¬ã§ãã
åçã®æ°åã¯ã####ãã®åŸã«èšèŒããŸãã
#### 0
|
75 |
ã«ã€ã«ã¯ããããã 15 åã®æãçŽã®æãå
¥ããããšãã§ããã¬ã©ã¹ç¶ã 2 å賌å
¥ããŸããããã®åŸãåãã¬ã©ã¹ç¶ãããã« 3 å賌å
¥ããŸãããã«ã€ã«ã¯ãã¹ãŠã®ã¬ã©ã¹ç¶ãåããããã«ãããã€ã®æãäœããªããã°ãªããŸãããïŒ
|
ã«ã€ã«ã賌å
¥ããã¬ã©ã¹ç¶ã®æ°ãèšç®ããŸãã
æåã«è³Œå
¥ããã¬ã©ã¹ç¶ã®æ°ã¯ 2 åã§ããããã« 3 åè²·ã£ãã®ã§ãåèšã¯æ¬¡ã®ããã«ãªããŸãïŒ
2 + 3 = 5 åã®ã¬ã©ã¹ç¶
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\[
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\]
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\]
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\]
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= 4 å¹
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ã¯ãªã¹ãã£ãŒã㯠3 å¹ã®ãããæã£ãŠããŸãã1 å¹ã®ãã㯠2 ãã£ãŒãã®é·ãã§ãããã 1 å¹ã®ãã㯠16 ã€ã³ãã®é·ãã§ãæåŸã®ãã㯠10 ã€ã³ãã®é·ãã§ãããã¹ãŠã®ããã®é·ããã€ã³ãã§åèšãããšãäœã€ã³ãã«ãªããŸããïŒ
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2å¹ç®ã®ããïŒ16 ã€ã³ã
3å¹ç®ã®ããïŒ10 ã€ã³ã
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24 ã€ã³ã + 16 ã€ã³ã + 10 ã€ã³ã = 50 ã€ã³ã
ãããã£ãŠããã¹ãŠã®ããã®é·ãã®åèšã¯ 50 ã€ã³ãã§ãã
åç㯠####50#### ã§ãã
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ãããªãŒã³ã¯ãããã 24 è²éçãå
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\[
5 \text{ ç®±} \times 24 \text{ æ¬} = 120 \text{ æ¬}
\]
次ã«ãåç®±ã®äœ¿çšç¶æ³ãèŠãŠãããŸãã
1. **2åã®ç®±**: 5/8ãæªäœ¿çšã§ãã
- 1ç®±ãããã®æªäœ¿çšã®è²éçã®æ°ã¯ \( 24 \times \frac{5}{8} = 15 \) æ¬ã§ãã
- ãããã£ãŠã2ç®±ã®æªäœ¿çšã®è²éçã®æ°ã¯ \( 15 \times 2 = 30 \) æ¬ã§ãã
2. **å¥ã®2åã®ç®±**: 2/3ãã䜿ãããŠããŸããã
- 䜿çšãããè²éçã®æ°ã¯ \( 24 \times \frac{2}{3} = 16 \) æ¬ã§ãã
- æªäœ¿çšã®è²éç㯠\( 24 - 16 = 8 \) æ¬ã§ãã
- ãããã£ãŠã2ç®±ã®æªäœ¿çšã®è²éçã®æ°ã¯ \( 8 \times 2 = 16 \) æ¬ã§ãã
3. **æåŸã®ç®±**: å®å
šã«äœ¿çšãããŠããŸããã
- æªäœ¿çšã®è²éçã®æ°ã¯ \( 24 \) æ¬ã§ãã
ãããããã¹ãŠè¶³ãåãããŠãæªäœ¿çšã®è²éçã®åèšãæ±ããŸãã
\[
30 \text{ æ¬} \, (+) \, 16 \text{ æ¬} \, (+) \, 24 \text{ æ¬} = 70 \text{ æ¬}
\]
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åçïŒ
#### 70
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çã㯠10 ã§ãã ####10
|
48 |
ããŒã«ã¯ãã£ããã³ã»ã¢ã¡ãªã«ã® 13 åã®å¹Žéœ¢ã§ãããã£ããã³ã»ã¢ã¡ãªã«ã¯ããŒã¿ãŒã»ããŒã«ãŒã® 7 åã®å¹Žéœ¢ã§ãã¢ã€ã¢ã³ãã³ã¯ããŒã¿ãŒã»ããŒã«ãŒãã 32 æ³å¹Žäžã§ããããŒã«ã 1456 æ³ã®å Žåãã¢ã€ã¢ã³ãã³ã¯äœæ³ã§ããïŒ
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\[
\text{ãã£ããã³ã»ã¢ã¡ãªã«ã®å¹Žéœ¢} = \frac{\text{ããŒã«ã®å¹Žéœ¢}}{13} = \frac{1456}{13} = 112
\]
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\[
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\]
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\[
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\]
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ããŒã·ãŒã®å¹Žéœ¢ = 2 à 8 = 16 æ³
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æšå¹Žã®ãã©ã¹ã®å¹Žéœ¢ = 3 à 15 = 45 æ³
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çã㯠46 ã§ãã®ã§ãæçµçãªåçã¯ä»¥äžã®éãã§ãïŒ
#### 46
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96 |
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- ããºãïŒ4å¹ Ã 3å¹ = 12å¹
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- ãŠãµã®ïŒ6å¹ Ã 3é±é = 18å¹
åãã®æ°ããããããæãŸããæ°ãåŒããŸãïŒ
- æ®ãã®ããºãïŒ100å¹ - 36å¹ = 64å¹
- æ®ãã®ãŠãµã®ïŒ50å¹ - 18å¹ = 32å¹
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- å¹³åäŸ¡æ Œ: 1000 ãã«
- å£²äž = 100 å° Ã 1000 ãã« = 100,000 ãã«
2. iPadã®å£²äž:
- å°æ°: 20 å°
- å¹³åäŸ¡æ Œ: 900 ãã«
- å£²äž = 20 å° Ã 900 ãã« = 18,000 ãã«
3. Apple TVã®å£²äž:
- å°æ°: 80 å°
- å¹³åäŸ¡æ Œ: 200 ãã«
- å£²äž = 80 å° Ã 200 ãã« = 16,000 ãã«
次ã«ã仿¥è²©å£²ããããã¹ãŠã®è£œåã®åèšå£²äžãèšç®ããŸãã
ç·å£²äžé« = iPhoneã®å£²äž + iPadã®å£²äž + Apple TVã®å£²äž
= 100,000 ãã« + 18,000 ãã« + 16,000 ãã« = 134,000 ãã«
次ã«ã販売ãããç·å°æ°ãèšç®ããŸãã
ç·å°æ° = iPhoneã®å°æ° + iPadã®å°æ° + Apple TVã®å°æ°
= 100 å° + 20 å° + 80 å° = 200 å°
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= 134,000 ãã« / 200 å° = 670 ãã«
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192 = x + 0.2x
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次ã«ããã¶ã®ç®±ã®åèšéé¡ãèšç®ããŸãã
ãã¶ã®ç®±ã®åèšéé¡:
\( 10 \text{ å} \times 14 \text{ ãã«/å} = 140 \text{ ãã«} \)
ããã§ã¯ãç·åèšéé¡ãæ±ããŸãã
ç·åèšéé¡:
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ã¡ã¢ãªãŒãæ¯æã£ãéé¡ã¯ 200 ãã«ã§ãããã圌女ã®ãé£ãã¯:
ãé£ã:
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ãããã£ãŠã圌女ã¯ãããã®ãé£ããåãåããŸãããïŒ
#### 30
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åç: ####15
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èŠãªç·Žç¿æéã¯10,000æéã§ãã
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1. 1幎ã¯365æ¥ã§ããã圌ã¯å¹Žã«2é±éã®äŒæãåãã®ã§ãç·Žç¿ããæ¥æ°ã¯ä»¥äžã®ããã«èšç®ããŸãïŒ
- 1幎ã®ç·Žç¿æ¥æ° = 365æ¥ - 14æ¥ïŒäŒæïŒ = 351æ¥
2. æææ¥ããéææ¥ã®éã®ç·Žç¿æ¥æ°ãæ±ããŸãïŒ
- 1é±éã¯5æ¥ïŒææããéæïŒç·Žç¿ããã®ã§ã1幎ã§ã¯æ¬¡ã®ããã«èšç®ããŸãïŒ
- 1幎ã®ç·Žç¿é±æ° = 351æ¥ Ã· 7æ¥ â 50é±ïŒç«¯æ°ã¯åãæšãŠïŒ
- 幎éã®ç·Žç¿æ¥æ° = 50é± Ã 5æ¥/é± = 250æ¥
3. 8幎ã§ã®ç·ç·Žç¿æ¥æ°ãèšç®ããŸãïŒ
- ç·ç·Žç¿æ¥æ° = 250æ¥/幎 à 8幎 = 2000æ¥
4. å¿
èŠãªæéã1æ¥ã«å¿
èŠãªç·Žç¿æéã«å€æããŸãïŒ
- 1æ¥ã«å¿
èŠãªç·Žç¿æé = ç·å¿
èŠæé ÷ ç·ç·Žç¿æ¥æ°
- 1æ¥ã«å¿
èŠãªç·Žç¿æé = 10,000æé ÷ 2000æ¥ = 5æé
ãããã£ãŠãã©ã³ãã£ã¯æ¯æ¥5æéç·Žç¿ããå¿
èŠããããŸãã
åçã¯ïŒ####5
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250 |
ãã€ã¯ãšãããã¯ãããã®çš®ãæ€ããŸãããæããã€ã¯ã¯ 50 çš®ã®ãããã®çš®ãæ€ãããããã¯ãã€ã¯ã® 2 åã®æ°ãæ€ããŸãããååŸããã€ã¯ã¯ 60 çš®ã®ãããã®çš®ãæ€ãããããã¯ãã€ã¯ãã 20 çš®å°ãªãæ°ãæ€ããŸããã圌ãã¯åèšã§ããã€ã®ãããã®çš®ãæ€ããŸãããïŒ
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ãŸãããã€ã¯ãæã«æ€ãããããã®çš®ã®æ°ã¯ 50 çš®ã§ãã
次ã«ãããããæã«æ€ãããããã®çš®ã®æ°ãèšç®ããŸãããããã¯ãã€ã¯ã® 2 åã®æ°ãæ€ããã®ã§ãããã㯠50 à 2 = 100 çš®ã®ãããã®çš®ãæ€ããŸããã
次ã«ãååŸã®æ€ããæ°ãèããŸãããã€ã¯ã¯ååŸã« 60 çš®ã®ãããã®çš®ãæ€ããŸããããããã¯ãã€ã¯ãã 20 çš®å°ãªãæ°ãæ€ããã®ã§ãããã㯠60 - 20 = 40 çš®ã®ãããã®çš®ãæ€ããŸããã
æåŸã«ãåèšã§äœçš®ã®ãããã®çš®ãæ€ããããèšç®ããŸãã
åèš = (ãã€ã¯ã®æã®çš® + ãããã®æã®çš®) + (ãã€ã¯ã®ååŸã®çš® + ãããã®ååŸã®çš®)
= (50 + 100) + (60 + 40)
= 150 + 100
= 250
ãããã£ãŠã圌ãã¯åèšã§ 250 çš®ã®ãããã®çš®ãæ€ããŸããã
åçïŒ####250
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