1964 AHSME Problems/Problem 14

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Problem

A farmer bought $749$ sheep. He sold $700$ of them for the price paid for the $749$ sheep. The remaining $49$ sheep were sold at the same price per head as the other $700$. Based on the cost, the percent gain on the entire transaction is:

$\textbf{(A)}\ 6.5 \qquad \textbf{(B)}\ 6.75 \qquad \textbf{(C)}\ 7 \qquad \textbf{(D)}\ 7.5 \qquad \textbf{(E)}\ 8$

Solution

Let us say each sheep cost $x$ dollars. The farmer paid $749x$ for the sheep. He sold $700$ of them for $749x$, so each sheep sold for $\frac{749}{700} = 1.07x$.

Since every sheep sold for the same price per head, and since every sheep cost $x$ and sold for $1.07x$, there is an increase of $\frac{1.07x - 1x}{1x} = 0.07$, or $7\%$, which is option $\box{\textbf{(C)}}$ (Error compiling LaTeX. ! Missing number, treated as zero.)

See Also

1964 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
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