Q22. - Algebra 1

Question

GASOLINE The average cost of regular gasoline in North Carolina increased by 73% from 2006 to 2007. If the average cost of a gallon of gas in 2006 was $2.069 what was the average cost in 2007? Round to the nearest cent.

Step-by-Step Solution

Answer

The average cost of a gallon of gasoline in 2007 was $3.58.

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 the average cost of gasoline in North Carolina is increased by 73%. And the average cost of gallons of gasoline in 2006 was $2.069.

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

If we let x represent the gas price in 2007 then, we can find the amount of change using the percentage change as follows:

$\begin{array}{l}x=73\%\times \$2.069+\$2.069\\ x=\frac{73}{100}\times 2.069+2.069\\ x=0.73\times 2.069+2.069\\ x=1.5103+2.069\\ x=\$3.5793\end{array}$

Thus, the average cost of a gallon of gasoline in 2007 was $3.58.