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2020 Math Kangaroo

Problem 8

Problem 8 · 2020 Math Kangaroo Medium
Ratios, Rates & Proportions proportionunit-rate

A dozen nanica bananas cost the same as ten prata bananas. If y nanica bananas cost x reais, how many reais do z prata bananas cost?

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Answer: C\(6xz\)\(5y\)
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Hint 1 of 2
First find the price of one nanica banana from 'y nanicas cost x reais'.
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Hint 2 of 2
Twelve nanicas cost the same as ten pratas, so one prata costs a bit more than one nanica — by what factor?
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Approach: price one banana, convert nanica price to prata price, then scale to z pratas
  1. From 'y nanicas cost x reais', one nanica costs \(\frac{x}{y}\) reais.
  2. Twelve nanicas (cost \(\frac{12x}{y}\)) equal ten pratas in price, so one prata costs \(\frac{12x}{10y} = \frac{6x}{5y}\) reais.
  3. Then z pratas cost \(z \cdot \frac{6x}{5y} = \frac{6xz}{5y}\) reais, which is option C.
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