Problem 18 · 2019 Math Kangaroo
Hard
Fractions, Decimals & Percents
ratioproportion
A 1-litre bottle of syrup is still half full. The syrup is to be diluted in the ratio 1 : 7 to make juice. Which fraction of the syrup should be used to obtain 2 litres of juice?
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Answer: B — 12
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Hint 1 of 2
Syrup : water = 1 : 7 means juice is 1/8 syrup.
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Hint 2 of 2
2 litres of juice needs 1/4 litre of syrup — compare to the 1/2 litre you have.
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Approach: find syrup needed, compare to amount on hand
- Juice is 1 part syrup to 7 water, so 1/8 of the juice is syrup.
- 2 litres of juice need 2 × (1/8) = 1/4 litre of syrup.
- You hold 1/2 litre, so you use (1/4)/(1/2) = 1/2 of the syrup.
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