PERCENT OF CHANGE LESSON 3.4 EXPLORE! MINIMUM WAGE In 2009, Washington had the highest minimum wage rate in the United States. The chart below gives the minimum wage in Washington from 2005 to 2009. Year 2005 2006 2007 2008 2009 Minimum Wage $7.35 $7.63 $7.93 $8.07 $8.55 Step 1: Find the change (difference) in the minimum wage from 2005 to 2006. Step 2: Find the ratio the nearest tenth. change in minimum wage minimum wage in 2005. Rewrite the ratio as a percent. Round to Step 3: Find the change (difference) in the minimum wage from 2006 to 2007. change in minimum wage minimum wage in 2006 Step 4: Find the ratio. Rewrite the ratio as a percent. Round to the nearest tenth. Step 5: Repeat this process to find the percent of change from 2007 to 2008 and from 2008 to 2009. Step 6: Compare the four percents. Between which years was there the greatest change in the minimum wage in terms of percent? Each ratio in the Explore! shows the amount of increase in the minimum wage compared to the original minimum wage. The answer is an example of a percent of change. The percent of change is the percent a quantity increases or decreases compared to the original amount. If the new amount is greater than the original amount, it is a percent of increase. If the new amount is less than the original amount, it is a percent of decrease. The change in the minimum wage above is an example of a percent of increase. 92 Lesson 3.4 ~ Percent of Change
EXAMPLE 1 Find the percent of increase from 10 to 18. Calculate the amount of increase. 18 10 = 8 Calculate the percent of increase. amount of increase = 8 = 0.8 = 80% original amount 10 The percent of increase from 10 to 18 is 80%. EXAMPLE 2 Find the percent of decrease from 25 to 21. Calculate the amount of decrease. 25 21 = 4 Calculate the percent of decrease. amount of decrease = 4 = 0.16 = 16% original amount 25 The percent of decrease from 25 to 21 is 16%. Always compare the amount of change to the original amount. In problems like Examples 1 and 2 the original amount is the first amount listed. In some situations you will know the percent of change but you may not know the amount of increase or decrease. When this is the case, you must solve the equation using inverse operations. The solution to the equation may not be the final answer to the problem. EXAMPLE 3 Last year 2,300 people attended a Fourth of July parade at the beach. This year the number of people increased by 8%. Find the number of people who attended the parade this year. You are given the percent increase. You need to find the amount of increase to add to the 2,300 people who attended last year. Use the percent of change equation. Write the percent of increase as a decimal. Multiply both sides by 2,300. amount of increase Percent of increase = original amount 0.08 = x 2300 184 = x There were 184 more people at this year s parade than at last year s parade. The number of people who attended the parade this year is 184 + 2300 = 2484. The total attendees at the parade this year was 2,484. Lesson 3.4 ~ Percent of Change 93
EXAMPLE 4 In 2007, Hernandez paid $2,000 for a new laptop computer. In 2012, Hernandez paid 60% less for a laptop computer than he had in 2007. Find the amount Hernandez paid for a laptop computer in 2012. The percent of decrease is given. Find the amount the laptop was decreased by to subtract it from the cost in 2007. Use the percent of change equation. Write the percent of decrease as a decimal. Multiply both sides by 2,000. Percent of decrease = amount of decrease original amount 0.6 = x 2000 1200 = x Hernandez paid $1,200 less in 2012 than in 2007. The amount he paid in 2012 is $2000 $1200 = $800. Hernandez paid $800 for a laptop computer in 2012. EXERCISES Identify the percent of change as an increase or a decrease. Find the percent of change. Round percents to the nearest tenth, if necessary. 1. 8 to 10 2. 15 to 18 3. 60 to 40 4. 120 to 60 5. 45 to 60 6. 95 to 80 7. 88 to 44 8. 4 to 12 9. 50 to 60 10. Fern found the percent of decrease from 80 to 60. Her work is shown below. Find her error and fix it. Solve the problem to find the percent of decrease from 80 to 60. 80 60 = 20 60 60 = 0. _ 3 = 33. _ 3 % 11. According to official census, the population in the United States reached 200 million in 1967. On October 17, 2006, the population in the United States reached 300 million. Find the percent of increase in the population of the United States from 1967 to 2006. 12. In 1980, approximately 12,400,000 students were enrolled in U.S. universities and colleges. In 2007, that number had increased by about 42%. Find the number of students enrolled in U.S. universities and colleges in 2007. 13. Can an amount be increased by more than 100%? Explain. 94 Lesson 3.4 ~ Percent of Change
14. Can an amount be decreased by more than 100%? Explain. 15. In 2004, there were 202 Democrats in the House of Representatives. In 2008, there were 256 Democrats in the House of Representatives. Find the percent of increase in the number of Democrats in the House of Representatives from 2004 to 2008. 16. The average price of gasoline was $1.29 in 1997 and $3.15 in 2007. Find the percent of increase. Round to the nearest tenth. 17. Stephanie collects teddy bears. Last year she had 20 bears in her collection and this year she has 24. Find the percent of increase. 18. In 2000, Roberto paid $1,500 for a digital camera. In 2013, he paid 70% less for a new digital camera. Find the amount Roberto paid for his new digital camera in 2013. 19. Last year 124 students took French. This year 25% fewer students took French. How many students are taking French this year? 20. One middle school sold $840 worth of plants during a fundraising event. They hope to increase their sales next year by 40%. How much money do they hope to raise? REVIEW 21. Two similar pentagons have a scale factor of 2 : 5. a. Find the ratio of their perimeters. b. Find the ratio of their areas. c. The smaller pentagon has an area of 12 cm². Find the area of the larger pentagon. 22. Two similar triangles have areas of 20 square feet and 45 square feet. a. Find the ratio of their areas. b. Find their scale factor. c. The larger triangle has a perimeter of 42 feet. Find the perimeter of the smaller triangle. 23. Violet made a scale drawing of her room. She used the scale 1 inch : 2 feet. One wall on her drawing has a length of 6 1_ inches. How long is her actual wall in feet? 4 Use a proportion or the percent equation to solve. 24. What is 30% of 90? 25. What is 75% of 80? 26. What percent is 24 of 36? 27. What percent is 12 of 15? 28. Twenty-two is 11% of what number? 29. Fifty-six is 14% of what number? Lesson 3.4 ~ Percent of Change 95
Tic-Tac-Toe ~ P e rce n t E r ror Percent error compares the result of a measurement made to its actual value. It shows the degree of error in a calculation or data. Suppose Erica measures a length and her result differs from its actual length by 10 cm. This is a close approximation if Erica was measuring the distance from New York to Los Angeles. However, if Erica was measuring a string with a length of 12 cm, her result is not close to the actual measurement. Knowing her measurement differed by 10 cm is not enough. How does the 10 cm compare to the actual measurement? Percent error better describes how close a measurement result is to the actual measurement by comparing the absolute value of the difference in the measurements to the actual measurement. Percent Error = Result Actual Value Actual Value 100 For example, Logan weighed a rock and found it to be 30 g. The actual rock weighed 29.7 g. What is the percent error in his measurement? Percent Error = 30 29.7 29.7 100 1.01% Logan s measurement differed from the actual measurement by an error of about 1%. In Exercises 1 5, find the percent error. 1. Cathy measured her volume of soda to be 10 oz when the can actually held 8 oz. 2. Talia measured her volume of water to be 30 oz when the bottle actually held 32 oz. 3. Laramie weighed a 500 g mass on a balance. He found it weighed 495 g. 4. Kit measured the length of a copper wire that was 60 cm long as 62 cm. 5. Theo measured the length of a string to be 10 cm when it was actually 9.98 cm. 6. Margo weighed a rock that was actually 20 g. Sam weighed a different rock that was 80 g. They both weighed their rocks and found them to be 2 g heavier than their actual weight. Find the percent error for each measurement. Why is the value of the percent error different when both results differed by 2 g? 96 Lesson 3.4 ~ Percent of Change