7-9 Percent Problems Warm Up Problem of the Day Lesson Presentation Course 1 Warm Up Problem of the Day Lesson Presentation

Write each decimal as a percent and fraction. Warm Up Write each decimal as a percent and fraction. 1. 0.38 2. 0.06 3. 0.2 19 50 __ 38%, 3 50 __ 6%, 1 5 __ 20%,

Problem of the Day Lucky Jim won $16,000,000 in a lottery. Every year for 10 years he spent 50% of what was left. How much did Lucky Jim have after 10 years? $15,625

Learn to find the missing value in a percent problem.

To find the percent one number is of another, use this proportion: % 100 = is of If you are looking for 45% of 420, 45 replaces the percent sign and 420 replaces “of.” The first denominator, 100, always stays the same. The “is” part is what you have been asked to find.

Additional Example 1: Application There are 560 students in Ella’s school. If 35% of the students participate in after-school sports, how many students participate in after-school sports? First estimate your answer. Think: 35% = , which is close to , and 560 is close to 600. So about of the students participate in after-school sports. 35 100 ___ 1 3 __ 1 3 __ • 600 = 200 This is the estimate. Helpful Hint Think: “35 out of 100 is how many out of 560?”

Additional Example 1 Continued Now solve: Let s represent the number of students who participate in after-school sports. 35 100 ___ s 560 ___ = 100 • s = 35 • 560 The cross products are equal. 100s = 19,600 s is multiplied by 100. 100s 100 ____ 19,600 100 _____ Divide both sides of the equation by 100 to undo multiplication. = s = 196 Since 196 is close to your estimate of 200, 196 is a reasonable answer. 196 students participate in after-school sports.

Check It Out: Example 1 There are 480 students in Tisha’s school. If 70% of the students participate in the fundraising program, how many students participate in the fundraising program? First estimate your answer. Think: 70% = , which is close to , and 480 is close to 500. So about of the students participate in after school sports. 70 100 ___ 3 4 __ 3 4 __ • 500 = 375 This is the estimate.

Check It Out: Example 1 Continued Now solve: Let s represent the number of students who participate in the fundraising program. 70 100 ___ s 480 ___ = 100 • s = 70 • 480 The cross products are equal. 100s = 33,600 s is multiplied by 100. 100s 100 ____ 33,600 100 _____ Divide both sides of the equation by 100 to undo multiplication. = s = 336 Since 336 is close to your estimate of 375, 336 is a reasonable answer. 336 students participate in the fundraising program.

Additional Example 2: Application Johan is 25% of the way through his exercises. If he has exercised for 20 minutes so far, how much longer does he have to work out? 25% of the exercises are completed, so 20 minutes is 25% of the total time needed. % 100 ___ is of __ = Set up a proportion. The “of” part is what you have been asked to find. 25 100 ___ 20 m __ = 100 • 20 = 25 • m The cross products are equal.

Additional Example 2 Continued m is multiplied by 25. 2,000 25 _____ 25m 25 ____ Divide both sides by 25 to undo multiplication. = 80 = m The time needed for the exercises is 80 min. So far, the exercises have taken 20 min. Because 80 – 20 = 60, Johan will be finished in 60 min.

Check It Out: Example 2 Phil is 30% of the way through his homework. If he has worked for 15 minutes so far, how much longer does he have to work? 30% of the exercises are completed, so 15 minutes is 30% of the total time needed. % 100 ___ is of __ = Set up a proportion. The “of” part is what you have been asked to find. 30 100 ___ 15 m __ = 100 • 15 = 30 • m The cross products are equal.

Check It Out: Example 2 Continued m is multiplied by 30. 1,500 30 _____ 30m 30 ____ Divide both sides by 30 to undo multiplication. = 50 = m The time needed for the homework is 50 min. So far, the homework has taken 15 min. Because 50 – 15 = 35, Phil will be finished in 35 min.

Instead of using proportions, you can also multiply to find a percent of a number.

Additional Example 3: Multiplying to Find a Percent of a Number Find 36% of 50. 36% = 0.36 Write the percent as a decimal. 0.36 • 50 Multiply using the decimal. 18 So 18 is 36% of 50. Check Use a model to check the answer. 0 5 10 15 20 25 30 35 40 45 50 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Write the percent as a decimal. Check It Out: Example 3 Find 20% of 70. 20% = 0.20 Write the percent as a decimal. 0.20 • 70 Multiply using the decimal. 14 So 14 is 20% of 70. Check Use a model to check the answer. 0 7 14 21 28 35 42 49 56 63 70 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Lesson Quiz 1. Find 28% of 310. 2. Find 70% of 542. 3. Martha is taking a 100-question test. She has completed 60% of the test in 45 minutes. How much longer will it take her to finish the test? 4. Crystal has a collection of 72 pennies. If 25% of them are Canadian, how many Canadian pennies does she have? 86.8 379.4 30 min 18