# 1985 AJHSME Problems/Problem 6

## 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 1

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 $\boxed{\text{D}}$

## Solution 2

We can set up a direct proportion relating the amount of sheets to the thickness because according to the problem, all the papers have the same thickness. Our proportion is $$\frac{5}{500}=\frac{7.5}{x}$$ where $x$ is the number we are looking for. Next, we cross-multiply to get $5x=500 \times 7.5$ so $x=750$ which is $\boxed{\text{D}}$

~GrantStar

## Video Solution

~savannahsolver

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