Socrates - Comenius 1:
School Project We are all living under the same sky
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Socrates - Comenius 1: |
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Mathematics
Fourth task
Three friends Adam, Bedrich and Cyril live in neighbouring small houses. They decided to supply themselves together with a lawn-mower that costs 15000 CZK. As their gardens are of different areas, they contributed to the purchase with different sums: Adam paid 6500 CZK, Bedrich 5500 CZK and Cyril paid the rest. They used the lawn-mower together three years. Then Bedψich and Cyril bought their own lawn-mowers, while Adam kept the old lawn-mower. The friends agreed that during the three years the price had fallen down to 9000 CZK. What amounts of money should Adam pay to Bedrich and Cyril?
Solution:
Using the rule of three, I reckoned how much money (in %) each of them gave for the purchase of the lawn-mower.
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Adam: |
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15000 CZK .. 100 % |
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6500 CZK ... .. . x % |
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6500 : 15000 |
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x : 100 |
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x |
= |
(6500 . 10) : 15000 |
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x |
= |
43 % |
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Bedrich: |
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15000 CZK .. 100 % |
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| 5500 CZK ... .. . y % | ||
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__________________________________ |
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| y | = | (5500 . 100) : 15000 |
| y | = | 37 % |
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Cyril: |
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| 15000 CZK .. 100 % | ||
| 3000 CZK ... .. . z % | ||
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| z | = | (3000 . 100) : 15000 |
| z | = | 20 % |
Then I reckoned (by the same method) how much money has Adam to give to Bedrich and Cyril.
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Adam gives to Bedrich: |
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| 9000 CZK .. 100 % | ||
| x CZK ... .. .. . 37 % | ||
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| x : 9000 | = | 37 : 100 |
| x | = | (9000 . 37) : 100 |
| x | = | 3300 CZK |
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Adam gives to Cyril: |
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| 9000 CZK .. 100 % | ||
| x CZK ... .. .. . 20 % | ||
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| x : 9000 | = | 20 : 100 |
| x | = | (20 . 9000) : 100 |
| x | = | 1800 CZK |
Adam should give 3300 CZK to Bedrich and 1800 CZK to Cyril.