If (3/5)=(M/45)=(60/N) , what is M+N ?

AMC 8 2008 Problem 7

AMC8 2008 年第 7 题

比与比例★☆☆☆☆

\displaystyle \frac{3}{5}=\frac{M}{45}=\frac{60}{N}

, what is M+N ?

如果

A.27
B.29
C.45
D.105
E.127

正确答案 · Correct Answer

解析 · Solution

Solution 1

Note that 𝑀 45 = 3 5 = 3.9 5.9 = 27 45 45 M = 5 3 = 5.9 3.9 = 45 27 , so 𝑀 = 27 M=27. Similarly, 60 𝑁 = 3 5 = N 60 = 5 3 = 3 ⋅ 20 5 ⋅ 20 = 60 100 5⋅20 3⋅20 = 100 60 , so 𝑁 = 100 N=100. The sum 𝑀 + 𝑁 = 27 + 100 = 127 M+N=27+100=127. OR OR Note that 𝑀 45 = 3 5 45 M = 5 3 , so 𝑀 = 3 5 ⋅ 45 = 27 M= 5 3 ⋅45=27. Also 60 𝑁 = 3 5 N 60 = 5 3 , so 𝑁 60 = 5 3 60 N = 3 5 , and 𝑁 = 5 3 ⋅ 60 = 100 N= 3 5 ⋅60=100. The sum ⁡ 𝑀 + 𝑁 = 27 + 100 = 127 sumM+N=27+100=127. Answer: 𝐸 E .

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