2009 AMC 8 Problems/Problem 21

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Problem

Andy and Bethany have a rectangular array of numbers 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 $\frac{A}{B}$?

$\textbf{(A)}\ \frac{64}{225}     \qquad \textbf{(B)}\   \frac{8}{15}    \qquad \textbf{(C)}\    1   \qquad \textbf{(D)}\   \frac{15}{8}    \qquad \textbf{(E)}\    \frac{225}{64}$

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