3 Rearrange the digits in . What Problem of the DayRearrange the digits in Whatfraction of the possible arrangements are true proportions?2613=13
4 Sunshine State Standards MA.7.A.1.2 Solve percent problems, including problems involving discounts…[and] taxes…
5 Sloths may seem lazy, but their extremely slow movement helps to make them almost invisible to predators. Sloths sleep an average of 16.5 hours a day. To find out what percent of a 24-hour day hours is, you can use a proportion or an equation.
6 Proportion Method Equation Method Partn16.5Part=What percent of 24 is 16.5?Whole10024Wholen · 24 = 100 · 16.5n · 24 = 16.524n = 1,650n =n = 68.75n = 68.75%Sloths spend about 69% of the day sleeping!
7 Additional Example 1A: Using Proportions to Solve Problems with Percents What percent of 40 is 25?n100=2540Write a proportion.n · 40 = 100 · 25Set the cross products equal.40n = 2,500Multiply.40n40= 2,50040Divide each side by 40 to isolatethe variable.n = 62.525 is 62.5% of 40.
8 Additional Example 1B: Using Proportions to Solve Problems with Percents 15 is 25% of what number?25100=15nWrite a proportion.n · 25 = 100 · 15Set the cross products equal.25n = 1,500Multiply.25n25= 1,50025Divide each side by 25 to isolatethe variable.n = 6015 is 25% of 60.
9 Check It Out: Example 1AFind the percent of each number.What percent of 320 is 40?n100=40320320n = 4,00012.5 = n12.5%
10 Check It Out: Example 1BFind the percent of each number.8 is 40% of what number?8n40100=40n = 800n = 2020
11 Additional Example 2A: Using Equations to Solve Problems with Percents 35 is 28% of what number?35 = 28% · nWrite an equation.35 = 0.28 · nWrite 28% as a decimal.350.280.28 · n0.28Divide each side by 0.28 to isolate the variable.=125 = n35 is 28% of 125.
12 Additional Example 2B: Using Equations to Solve Problems with Percents What percent of 9 is 18?18 = n · 9Write an equation.189n · 99Divide each side by 9 to isolate the variable.=2 = nWrite the decimal as a percent.200% = n18 is 200% of 9.
13 Check It Out: Example 2ASolve.9 is 75% of what number?9 = 0.75 · n90.75=0.75n12 = n
14 Check It Out: Example 2BSolve.24 is 150% of what number?14 = n241.51.5n1.5=16 = n
15 Additional Example 3: Consumer Application Raoul found a pair of shoes that were marked down to 80% of the original price. He had a coupon that gave him an additional $10 off the shoes. The sales tax rate was 6.5% and Raoul paid $5.46 in sales tax. What was the original price of the pair of shoes?Work backward. Find the final price of the shoes.6.5% of price is $5.46.Write a word sentence.0.065 x = 5.46Write an equation.Divide both sides byx = 84The price of the shoes with the coupon was $84.
16 Additional Example 3 Continued Find the price of the shoes without the coupon.= 94The price of the shoes was $94 after it was marked down to 80% of the original price. Find the original price.80% of price is $94.Write a word sentence.0.8 x = 94Write an equation.Divide both sides by 0.8.x = 117.5The original price of the shoes was $
17 Check It Out: Example 3AMarie-Claire bought a scarf marked down to 75% of its original price. She had a coupon that gave her an additional $5 off the scarf. The sales tax rate was 6%, and Marie-Claire paid $1.35 in sales tax. What was the originalprice of the scarf?Find the price before the sales tax was applied: = x1.350.060.06x=$22.50 = x
18 Check It Out: Example 3A Continued Find the price before Marie used her $5 coupon: = $27.50Find the price before the markdown: · x = 27.500.75x0.7527.50x0.75=x = 36.67The original price of the scarf was $36.67.
19 Check It Out: Example 3BIn 2008, Brenda made $42,756, which was 105% of what she made in In 2007, she made $4,000 more than she made in The amount she made in 2006 was 102% of what she made in How much did Brenda make in 2005?Find what she made in 2007: ,756 = x42,7561.051.05x=$40,720 = x
20 Check It Out: Example 3B Continued Find what she made in 2006: 40,720 - $4,000 = $36,720Find what she made in 2005: 36,720 = x36,720x1.021.02x1.02=36,000 = xBrenda made $36,000 in 2005.
21 Additional Example 4: Finding Sales Tax A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18?Restate the question: What percent of $225 is $18?n10018225=Write a proportion.n · 225 = 100 · 18Set the cross products equal.225n = 1800Multiply.225n2251800225=Divide each side by 225.n = 88% of $225 is $18. The sales tax is 8%.
22 Check It Out: Example 4AJarell paid $25.56 for his new bookbag. The amount he paid included a sales tax of $1.56. Find the sales tax rate.n100=1.562430n = 1.56(100)The sales tax rate is 6.5%.Price before sales tax: = $2424n156n = 0.065
23 Check It Out: Example 4BLisa paid $11 sales tax for a bike. If the sales tax rate was 5.5%, how much did the bike cost without the sales tax?11 = xThe bike cost $200 without sales tax.110.055=0.055 x200 = x
24 Lesson QuizzesStandard Lesson QuizLesson Quiz for Student Response Systems
25 Lesson QuizSolve.1. 21 is 42% of what number?2. What percent of 292 is 73?3. 112% of what number is 84?4. What percent of 1,340 is 13.4?5. An ad features a bicycle on sale for $139. If the total cost of the bike is $147.34, what is the sales tax rate?5025%751%6%
26 Lesson Quiz for Student Response Systems 1. Solve. 19 is 38% of what number?A. 69B. 50C. 38D. 34
27 Lesson Quiz for Student Response Systems 2. What percent of 170 is 51?A. 25%B. 30%C. 40%D. 50%
28 Lesson Quiz for Student Response Systems 3. 128% of what number is 96?A. 25B. 50C. 75D. 96
29 Lesson Quiz for Student Response Systems 4. What percent of 1,520 is 15.2?A. 25%B. 15%C. 10%D. 1%
30 Lesson Quiz for Student Response Systems 5. A jeweler has a pendant on sale for $150. If the total cost of the pendant is $160.50, what is the sales tax rate?A. 6%B. 7%C. 8%D. 9%