High School Math : Setting up Expressions

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Expressions

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

Possible Answers:

\(\displaystyle \frac{1}{2}\)

\(\displaystyle 1\)

\(\displaystyle \frac{3}{4}\)

\(\displaystyle \frac{4}{3}\)

\(\displaystyle 0\)

Correct answer:

\(\displaystyle \frac{3}{4}\)

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 \(\displaystyle 1.5X\).

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

or

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

The ratio of \(\displaystyle Z\) to \(\displaystyle X\) is then:

\(\displaystyle \frac{.5*1.5*X}{X}\)

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

  \(\displaystyle \frac{3}{4}\) .

Learning Tools by Varsity Tutors