Q2. - Algebra 1

Question

TUITION A recent percent of the increase in tuition at Northwestern University, in Evanston, Illinois, was 5.4%. If the new cost is $\$33,408$ per year, find the original cost per year.

Step-by-Step Solution

Answer

The original cost per year is 31696.39.

Step 1. Use the definition of the percentage change.

The percent change is the increase or decrease in the value of a quantity. If the new value is larger than the original value then it is a percent increase and if the change in value is lesser than the original value it is called percentage decrease.

Step 2. Example of the percentage change.

For example, if a person has 25 dollars and he gets 3 more dollars and now has 28 dollars, its percentage increase is calculated as shown:

$\begin{array}{l}\text{Increase }=28-25=3\\ \%\text{ change = r, then}\\ \frac{3}{25}=\frac{r}{100}\\ r=\frac{3}{25}\times 100\\ =12\%\end{array}$

  

Step 3. Find the percentage change.

We are given that

 $\begin{array}{l}\begin{array}{l}\text{Original}:x\\ \text{New}:\$33,408\end{array}\\ r=5.4\%\end{array}$

This is a percent of increase because the new amount is more than the original. 

We find the amount of change. And calculate the percentage change as follows:

$\begin{array}{l}\text{Change }=33408-x\\ \frac{33408-x}{x}=\frac{5.4}{100}\\ \frac{33408-x}{x}=0.054\\ 33408-x=0.054x\\ 33408=0.054x+x\\ 33408=1.054x\\ x=\frac{33408}{1.054}\\ x=31696.39\end{array}$

Thus the original cost per year is 31696.39.