AMC 8 2009 Problem 21

AMC8 2009 年第 21 题

比与比例★★★☆☆

Andy and Bethany have a rectangular array of numbers greater than 0 with 40 rows and 75 columns. Andy adds the numbers in each row. The average of his 40 sums is A . Bethany adds the numbers in each column. The average of her 75 sums is B . What is the value of

\displaystyle \frac{A}{B}

Andy 和 Bethany 有一张 40 行 75 列的矩形正数阵列，Andy 把每行的数字都相加，得到的 40 个和的平均值是 A。Bethany 把每列的数字都相加，所得的 75 个和的平均值是 B。那么多少？

A. $\displaystyle \frac{64}{225}$
B. $\displaystyle \frac{8}{15}$
C.1
D. $\displaystyle \frac{15}{8}$
E. $\displaystyle \frac{225}{64}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

Note that

40A = 75B = \text{sum of the numbers in the array}

. This means that

\displaystyle \frac{A}{B} = \text{(D) } \frac{15}{8}

using basic algebraic manipulation.

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