Problem 20 · 2014 Math Kangaroo
Stretch
Fractions, Decimals & Percents
percent-multiplier
The average of two positive numbers is 30% less than one of the two numbers. By what percentage is the average bigger than the other number?
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Answer: A — 75%
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Hint 1 of 2
Call the larger number a; the average is 30% below it, so the average equals 0.7a.
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Hint 2 of 2
Use average = (a + b)/2 to find b, then compare the average with b.
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Approach: express both numbers through the average
- Let a be the larger number. The average is 30% less, so average = 0.7a.
- Since average = (a + b)/2, we get 0.7a = (a + b)/2, so b = 0.4a.
- The average exceeds b by (0.7a − 0.4a) ÷ 0.4a = 0.3a/0.4a = 0.75.
- So the average is 75% bigger than the other number.
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