Question

Find the percent increase.

In$1995$, the standard bus fare in Chicago was \($1.50$. Inrole="math" localid="1647116743463" $2008$, the standard bus fare was \)$2.25$.

Short answer

If bus fare in $1995$was $$1.5$and Bus fare in $2008$was $$2.25$then the increase in bus fare might be$50\%.$

Step-by-step solution

Step 1. Given information    

bus fare in $1995$was $$1.50$

Bus fare in$2008$was $$2.25$

Step 2. Increase amount 

An increase in the amount of bus fare is the difference between the new bus fare and the old bus fare.

Consider i is the increase in the bus fare.

Increase $=$new bus fare $-$old bus fair

$$\begin{gathered} i=2.25-1.50 \\ i=0.75 \end{gathered}$$

So the increase in the bus fare is $$0.75$.

Step 3. Percent increase 

Consider Percent increase is P.

Increase amount is what Percent of old bus fare

$0.75$is what percent of $1.50$

$$\begin{gathered} 0.75=P\times 1.50 \\ \frac{0.75}{1.50}=P \\ 0.5=P \\ P=50\% \end{gathered}$$

so percent increase in bus fare is$50\%.$

Step 4. Verification 

$0.75$is half of $1.50$

$0.75$is $50\%$of $1.50$

so role="math" localid="1647117406608" $50$percent increase in the bus fare is correct.