Problem 15 · 2014 Math Kangaroo
Medium
Fractions, Decimals & Percents
proportionwork-backward
The tail of the biggest crocodile in a zoo is one third of the crocodile’s total length. The head is 93 cm long and makes up one quarter of the length of the crocodile not counting its tail. How long is the crocodile?
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Answer: A — 558 cm
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Hint 1 of 2
Tail is 1/3 of the whole, so the rest (head + body) is 2/3 of the whole.
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Hint 2 of 2
The head is 1/4 of that 'rest', and the head is 93 cm.
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Approach: chain the two fractions back to the total
- Without the tail the crocodile is 2/3 of the total length.
- The head is 1/4 of that part: 93 = (1/4)(2/3 L) = L/6, so L = 558.
- The crocodile is 558 cm long.
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