Problem 14 · 2013 Math Kangaroo
Hard
Algebra & Patterns
substitutionpercent-multiplier
A class has written a test. If every boy had obtained 3 more points, the class average would be 1.2 points higher than it is now. What percentage of the children in this class are girls?
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Answer: D — 60%
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Hint 1 of 2
Giving every boy 3 more points adds 3 × (number of boys) to the class total.
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Hint 2 of 2
That extra total, spread over all children, is the 1.2-point rise — set up the equation for the fraction of boys.
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Approach: relate the total point increase to the average increase
- If there are b boys among c children, adding 3 to each boy adds 3b points total.
- The average rises by 3b / c = 1.2, so b / c = 0.4 — 40% are boys.
- Therefore 60% are girls.
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