Setting up Expressions

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Math › Setting up Expressions

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1

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

$\frac{3}{4}$

$\frac{4}{3}$

$\frac{1}{2}$

Explanation

If the original price of the T-shirt is , increasing the price by 50% means that the new price is 150% of , or .

If the price is then decreased by 50%, the new price is 50% of

or

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

The ratio of to is then:

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

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

$\frac{3}{4}$ .

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