Problem 7 · 2014 AMC 8
Easy
Algebra & Patterns
sum-and-difference
There are four more girls than boys in Ms. Raub's class of 28 students. What is the ratio of number of girls to the number of boys in her class?
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Answer: B — 4 : 3.
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Hint 1 of 2
Picture setting the 4 extra girls aside first. The remaining 28 − 4 = 24 students split evenly into boys and (the rest of the) girls.
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Hint 2 of 2
That gives the smaller group = (sum − difference)/2; add the 4 back for the larger group.
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Approach: sum-and-difference (peel off the gap, then split evenly)
- Set aside the 4 "extra" girls. The other 24 students are half boys, half girls: 12 each. So boys = 12, girls = 12 + 4 = 16.
- Ratio girls : boys = 16 : 12 = 4 : 3.
- Reusable formula: with a known sum S and difference D, the two amounts are (S+D)/2 and (S−D)/2 — no equation-solving needed.
Another way — one equation:
- Let boys = b; girls = b + 4. Then b + (b + 4) = 28, so 2b = 24 and b = 12.
- Girls = 16, ratio = 16 : 12 = 4 : 3.
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