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2014 Math Kangaroo

Problem 9

Problem 9 · 2014 Math Kangaroo Easy
Ratios, Rates & Proportions ratioproportion

In Kangaroo City there are m men, f women and k children, with m : f = 2 : 3 and f : k = 8 : 1. In what ratio is the number of adults (men and women) to the number of children?

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Answer: E — 40 : 3
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Hint 1 of 2
Scale the two ratios so the women count matches in both.
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Hint 2 of 2
Make f the same number, then read off adults vs children.
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Approach: line up the shared term (women)
  1. m : f = 2 : 3 and f : k = 8 : 1. Scale the first so f = 24: m : f = 16 : 24.
  2. Then k = 3, and adults = m + f = 16 + 24 = 40.
  3. Adults : children = 40 : 3, so 40 : 3.
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