In the last section, you used percent bars and proportions to make calculations involving percents. In this section, you will apply that approach to solving problems involving percent increase or percent decrease.

Use the interactive below to complete the table that follows. Click on the image to open the interactive in a new browser tab or window. Enter the percent of increase or decrease, and observe both the change in the bar height and the expression used to calculate the new values. Use the information in the interactive to complete the table that follows.

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Copy the table below on a piece of paper. Use the interactive to complete the table, and then use the completed table to answer the conclusion questions that follow.

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Percent of Increase	Expression	New Value	Percent of Decrease	Expression	New Value
10%	1.1 × 5	5.5	50%	0.5 × 5	2.5
20%	1.2 × 5	6	40%	0.6 × 5	3
30%	1.3 × 5	6.5	30%	0.7 × 5	3.5
40%	1.4 × 5	7	20%	0.8 × 5	4
50%	1.5 × 5	7.5	10%	0.9 × 5	4.5

Conclusion Questions

• How does the percent of increase compare to the expression used to calculate the new value?

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  If the percent is converted to a decimal, then the expression is (1 + percent) × 5.

• How does the new value compare to the original value and the percent of increase?

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  The new value is equal to the original value, 5, plus the percent of 5 represented by the percent of increase.

• How does the percent of decrease compare to the expression used to calculate the new value?

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  If the percent is converted to a decimal, then the expression is (1 − percent) × 5.

• How does the new value compare to the original value and the percent of decrease?

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  The new value is equal to the original value, 5, minus the percent of 5 represented by the percent of decrease.

• Suppose that the original value was 20 instead of 5. How much would a 35% increase from 20 represent?

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  A 35% increase from 20 would represent an increase of 20 × 0.35 = 7.

• Suppose that the original value was 20, and the new value was 25. What percent increase does this change represent?

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  How much does 20 increase to become 25?
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  25 − 20 = 5, so the new value is 5 greater than the original value. The original value is 20, so the new value is 5 over 20 5 20 = 25% greater than the original value. This change represents a 25% increase.

Pause and Reflect

When you are calculating the percent increase, should you compare the difference to the original value or the new value? Why?

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Compare the difference to the original value because the original value is the starting point for the change.

How would you calculate the percent decrease?

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Determine the difference between the original value and the new value, and then write the ratio of this difference to the original value. Convert the ratio to a percent.

Generalize a formula that you could use to calculate the percent increase or decrease.

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Final Value - Starting Value over Starting Value Final Value − Starting Value Starting Value = Percent Change over 100 Percent Change 100

Percent Change = Final Value - Starting Value over Starting Value Final Value − Starting Value Starting Value × 100%

Practice

1. Vanessa is selling cookies for her scouting troop. Last week, she sold 45 boxes of cookies. This week, she sold 54 boxes. What is the percent increase of sales from last week to this week?

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   Final Value - Starting Value over Starting Value Final Value − Starting Value Starting Value = Percent Change over 100 Percent Change 100
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   There is a 20% increase in sales from last week to this week.
2. Yesterday, one share of stock in Peartree Oil Services sold for $37.75. Today, the price of one share of stock at the end of the day was $36.50. What is the approximate percent change in the value of one share of stock? Round your answer to the nearest tenth of a percent.

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   Final Value - Starting Value over Starting Value Final Value − Starting Value Starting Value = Percent Change over 100 Percent Change 100
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   There is a 3.3% decrease in the price of one share of stock.
3. This week, there were 10,000 visitors to the Lincoln Zoo. If the zoo manager would like for there to be a 15% increase in the number of visitors next week, how many visitors should there be in order to reach this goal?

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   Determine the number of visitors that represents a 15% increase from 10,000, and then add that number back to the 10,000 visitors from this week.
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   15% × 10,000 = 0.15 × 10,000 = 1,500 more visitors
   10,000 + 1,500 = 11,500
   
   There should be 11,500 visitors next week in order to have a 15% increase from the number of visitors this week.