1955 AHSME Problems/Problem 5

Problem

$5y$ varies inversely as the square of $x$ . When $y=16, x=1$ . When $x=8, y$ equals:

$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 128 \qquad \textbf{(C)}\ 64 \qquad \textbf{(D)}\ \frac{1}{4} \qquad \textbf{(E)}\ 1024$

Solution

An inverse variation can be expressed in the form $xy = n$ , where $n$ is any number (except perhaps zero). Since $5y$ varies inversely with the square of $x$ , this particular one will be $5yx^2 = n$ .

We can plug in $16$ for $y$ and $1$ for $x$ , which makes $n=80$ . The equation is now $5yx^2 = 80$ .

When $x = 8$ , we can solve for $y$ using the equation $320y = 80$ , which makes $y$ $\boxed{\textbf{(D)} \frac{1}{4}}$ .

1955 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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1955 AHSME Problems/Problem 5

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