Problem 15 · 2012 Math Kangaroo
Medium
Algebra & Patterns
total-then-divide
In one class a test did not yield a very successful result because the average mark was exactly 4. The boys have done slightly better with an average mark of 3.6, while the girls have received an average mark of 4.2. Which of the following statements is correct?
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Answer: C — There are twice as many girls as boys.
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Hint 1 of 2
Write the total of all marks two ways: as 4×(everyone) and as boys' total plus girls' total.
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Hint 2 of 2
Set them equal and the ratio of boys to girls drops out.
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Approach: balance the weighted average
- With \(b\) boys and \(g\) girls, the total of all marks is \(3.6b + 4.2g\) and also \(4(b+g)\).
- So \(3.6b + 4.2g = 4b + 4g\), giving \(0.2g = 0.4b\), hence \(g = 2b\).
- There are twice as many girls as boys, choice C.
Mark:
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