1985 AJHSME Problems/Problem 14

Problem

The difference between a $6.5\%$ sales tax and a $6\%$ sales tax on an item priced at <dollar/> $20$ before tax is

$\text{(A)}$ <dollar/> $.01$

$\text{(B)}$ <dollar/> $.10$

$\text{(C)}$ <dollar/> $.50$

$\text{(D)}$ <dollar/> $1$

$\text{(E)}$ <dollar/> $10$

Solution

The most straightforward method would be to calculate both prices, and subtract. But there's a better method...

Before we start, it's always good to convert the word problems into expressions, we can solve.

So we know that the price of the object after a $6.5\%$ increase will be $20 \times 6.5\%$ , and the price of it after a $6\%$ increase will be $20 \times 6\%$ . And what we're trying to find is $6.5\% \times 20 - 6\% \times 20$ , and if you have at least a little experience in the field of algebra, you'll notice that both of the items have a common factor, $20$ , and we can factor the expression into $\begin{align*} (6.5\% - 6\% ) \times 20 &= (.5\% )\times 20 \\ &= \frac{.5}{100}\times 20 \\ &= \frac{1}{200}\times 20 \\ &= .10 \\ \end{align*}$

$.10$ is choice $\boxed{\text{B}}$

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1985 AJHSME Problems/Problem 14

Problem

Solution

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