Question

Find the percent increase. (Round to the nearest tenth of a percent.)

In$2011$, the IRS increased the deductible mileage cost to $55.5$cents from $50$cents.

Short answer

If IRS increased the deductible mileage cost from$50$cents to$55.5$cents the percent increase will be$11\%.$

Step-by-step solution

Step 1. Given information   

The old deductible mileage cost is $51$cents.

The new deductible mileage cost is $55.5$cents.

Step 2. Increase amount

An increase in the amount of deductible mileage cost is the difference between new cost and old cost.

Consider i is the increase in the amount of deductible mileage cost

Increase$=$new cost$-$old cost

$$\begin{gathered} i=55.5-50 \\ i=5.5 \end{gathered}$$

So increase in the amount of deductible mileage cost is $5.5$cents.

Step 3. Percent increase

Consider Percent increase is P.

Increase amount is what Percent of old cost

$5.5$is what percent of $50$

$$\begin{gathered} 5.5=P\times 50 \\ \frac{5.5}{50}=P \\ 0.11=P \\ P=11\% \end{gathered}$$

so percent increase in deductible mileage cost is$11\%.$

Step 4. Verification

$5.5$is $11\%$of

$$\begin{gathered} 5.5=0.11\times a \\ \frac{5.5}{0.11}=a \\ 50=a \end{gathered}$$

$5.5$is $11\%$of old cost

so $11\%$increase in deductible mileage cost is correct.