Problem 21 · 2015 Math Kangaroo
Stretch
Fractions, Decimals & Percents
percent-multipliersum-constraint
In a group of kangaroos the two lightest ones weigh 25 % of the total weight of the whole group. The three heaviest ones weigh 60 % of the total weight. How many kangaroos are in this group?
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Answer: A — 6
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Hint 1 of 2
The 2 lightest take 25% and the 3 heaviest take 60%, so the rest share the remaining percent.
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Hint 2 of 2
Find the leftover percentage and how many average-weight kangaroos it represents to total the group.
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Approach: account for every percent of the weight
- The 2 lightest are 25% and the 3 heaviest are 60%, leaving 15% for the kangaroos in between.
- A lightest one averages 12.5% and a heaviest one averages 20%, so each middle kangaroo must weigh between 12.5% and 20%.
- Only one middle kangaroo fits the leftover 15% (two would average 7.5% each, too light), giving 2 + 1 + 3 = 6 kangaroos.
- So there are 6 (A) kangaroos.
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