Finding Percent Increase and Percent Decrease

Finding Percent Increase and Percent Decrease

People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.

To find the percent increase, first we find the amount of increase, the difference of the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.

Example

In 2011, the California governor proposed raising community university fees from $26 a unit to $36 a unit. Find the percent increase. (Round to the nearest tenth of a percent.)

Solution

Step 1. Read the problem.
Step 2. Identify what we are looking for.		The percent increase
Step 3. Name what we are looking for.
Choose a variable to represent it.		Let \(p=\) the percent.
Step 4. Translate. Write a sentence that gives the information to find it.
First find the amount of increase.		new amount − original amount = increase
		\(36-26=10\)
Find the percent.		Increase is what percent of the original amount?
Translate into an equation.
Step 5. Solve the equation.
Divide by 26.
Change to percent form; round to the nearest tenth.
Step 6. Check. Does this make sense?
Yes, 38.4% is close to \(\frac{1}{3}\), and 10 is close to \(\frac{1}{3}\) of 26.
Step 7. Answer the question with a complete sentence.		The new fees represent a 38.4% increase over the old fees.

Notice that we rounded the division to the nearest thousandth in order to round the percent to the nearest tenth.

Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference of the original amount and the new amount. Then we find what percent the amount of decrease is of the original amount.

Example

The average price of a gallon of gas in one city in June 2014 was $3.71. The average price in that city in July was $3.64. Find the percent decrease.

Solution

Step 1. Read the problem.
Step 2. Identify what we are looking for.		the percent decrease
Step 3. Name what we are looking for.
Choose a variable to represent that quantity.		Let \(p=\) the percent decrease.
Step 4. Translate. Write a sentence that gives the information to find it.
First find the amount of decrease.		\(3.71-3.64=0.07\)
Find the percent.		Decrease is what percent of the original amaount?
Translate into an equation.
Step 5. Solve the equation.
Divide by 3.71.
Change to percent form; round to the nearest tenth.
Step 6. Check. Does this make sense?
Yes, if the original price was $4, a 2% decrease would be 8 cents.
Step 7. Answer the question with a complete sentence.		The price of gas decreased 1.9%.