Q39. - Algebra 1

Question

CONSUMER PRICE INDEX An index measures the percent change of a value from a base year. An index of 115 means that there was a 15% increase from the base year. In 2000, the consumer price index of dairy products was 160.7. In $2005, it was 182.4. Determine the percent of change.

Step-by-Step Solution

Answer

The percent of change is 13.50%.

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 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 Consumer price index in 2000 for dairy products was 160.7 and

in 2005, it was 182.4.

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

If we let x represent the percentage change then, we can find the amount of change as follows:

$\begin{array}{l}\text{Change :182.4 - 160.7 = 21.7 points.}\\ \text{Percent Change :}\frac{21.7}{160.7}\left(100\%\right)\\ =0.135\left(100\%\right)\\ =13.50\%\end{array}$

Thus, the percent of change is 13.50%.