1985 AJHSME Problems/Problem 6

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Problem

A ream of paper containing $500$ sheets is $5$ cm thick. Approximately how many sheets of this type of paper would there be in a stack $7.5$ cm high?

$\text{(A)}\ 250 \qquad \text{(B)}\ 550 \qquad \text{(C)}\ 667 \qquad \text{(D)}\ 750 \qquad \text{(E)}\ 1250$

Solution

We could solve the first equation for the thickness of one sheet of paper, and divide into the 2nd equation (which is one way to do the problem), but there are other ways, too.

Let's say that $500\text{ sheets}=5\text{ cm}\Rightarrow \frac{500 \text{ sheets}}{5 \text{ cm}} = 1$ . So by multiplying $7.5 \text{ cm}$ by this fraction, we SHOULD get the number of sheets in 7.5 cm. Solving gets

$\begin{align*}\frac{7.5 \times 500}{5} &= 7.5 \times 100 \\&= 750 \text{ sheets} \\\end{align*}$

$750$ is $\boxed{\text{D}}$

1985 AJHSME (Problems • Resources)
Preceded by Problem 5	Followed by Problem 7
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1985 AJHSME Problems/Problem 6

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