2008 AMC 8 Problem 7

Attempt Problem 7 of the 2008 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

7.

If 35=M45=60N,\dfrac{3}{5}=\dfrac{M}{45}=\dfrac{60}{N}, what is M+N?M+N?
 27 \ 27
 29 \ 29
 45 \ 45
 105 \ 105
 127 \ 127
Answer: E
Concepts:fractionratio and proportion
Small hint:
Solve for MM using M45=35\frac{M}{45}=\frac{3}{5}.
Big hint:
Solve for NN using 60N=35\frac{60}{N}=\frac{3}{5}, then add.
Solution:
From 35=M45\dfrac{3}{5}=\dfrac{M}{45}, we get M=3⋅455=27M=\dfrac{3\cdot45}{5}=27.
From 35=60N\dfrac{3}{5}=\dfrac{60}{N}, we get 3N=3003N=300, so N=100N=100.
Therefore, M+N=27+100=127M+N=27+100=127.
Thus, E is the correct answer.
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