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High School Math : Setting up Expressions

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Example Question #1 : Expressions

In April, the price of a t-shirt is $\$X$ $\displaystyle \$X$. In May, the store increases the price by 50%, so that the new price is $\$Y$ $\displaystyle \$Y$. Then in June, the store decreases the price by 50%, so that the t-shirt price is now $\$Z$ $\displaystyle \$Z$. What is the ratio of $\displaystyle Z$ to $\displaystyle X$ ?

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 1$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{4}{3}$ $\displaystyle \frac{4}{3}$

$\displaystyle 0$

Correct answer:

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

Explanation:

If the original price of the T-shirt is $\displaystyle X$, increasing the price by 50% means that the new price $\displaystyle Y$ is 150% of $\displaystyle X$, or 1.5X $\displaystyle 1.5X$.

If the price is then decreased by 50%, the new price $\displaystyle Z$ is 50% of $\displaystyle Y$

$.5\cdot (1.5X)=.75X$ $\displaystyle .5\cdot (1.5X)=.75X$

The ratio of $\displaystyle Z$ to $\displaystyle X$ is then:

$\frac{.5*1.5*X}{X}$ $\displaystyle \frac{.5*1.5*X}{X}$

The $\displaystyle X$'s in the numerator and denominator cancel, leaving $.5\cdot 1.5$ $\displaystyle .5\cdot 1.5$, or

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$ .

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High School Math : Setting up Expressions

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Example Question #1 : Expressions

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