Q5. - Algebra 1

Question

GEOGRAPHY The distance from Phoenix to Tucson is 120 miles. The distance from Phoenix to Flagstaff is about 21.7% longer. To the nearest mile, what is the distance from Phoenix to Flagstaff?

Step-by-Step Solution

Answer

The distance between Phoenix and Flagstaff is 146 miles.

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.

Let the distance between Phoenix and Flagstaff be x.

It is given that the distance between Phoenix to Flagstaff is 21.7% longer than the distance between Phoenix to Tucson, which is 120 miles, thus

 $\begin{array}{l}x=21.7\%\text{ of }120+120\\ x=\frac{21.7}{100}\times 120+120\\ x=0.217\times 120+120\\ x=26.04+120\\ x=146.04\text{ miles}\\ \approx \text{146 miles}\end{array}$

Thus, the distance between Phoenix and Flagstaff is 146 miles.