Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Solve. 1. 4x = 90 2. 8x = 96 3. 12x = 180 4. 26x = 182 22.5 12 15 7

Rearrange the digits in . What Problem of the Day Rearrange the digits in . What fraction of the possible arrangements are true proportions? 2 6 1 3 = 1 3

Sunshine State Standards MA.7.A.1.2 Solve percent problems, including problems involving discounts…[and] taxes…

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 16.5 hours is, you can use a proportion or an equation.

Proportion Method Equation Method Part n 16.5 Part = What percent of 24 is 16.5? Whole 100 24 Whole n · 24 = 100 · 16.5 n · 24 = 16.5 24n = 1,650 n = 0.6875 n = 68.75 n = 68.75% Sloths spend about 69% of the day sleeping!

Additional Example 1A: Using Proportions to Solve Problems with Percents What percent of 40 is 25? n 100 = 25 40 Write a proportion. n · 40 = 100 · 25 Set the cross products equal. 40n = 2,500 Multiply. 40n 40 = 2,500 40 Divide each side by 40 to isolate the variable. n = 62.5 25 is 62.5% of 40.

Additional Example 1B: Using Proportions to Solve Problems with Percents 15 is 25% of what number? 25 100 = 15 n Write a proportion. n · 25 = 100 · 15 Set the cross products equal. 25n = 1,500 Multiply. 25n 25 = 1,500 25 Divide each side by 25 to isolate the variable. n = 60 15 is 25% of 60.

Check It Out: Example 1A Find the percent of each number. What percent of 320 is 40? n 100 = 40 320 320n = 4,000 12.5 = n 12.5%

Check It Out: Example 1B Find the percent of each number. 8 is 40% of what number? 8 n 40 100 = 40n = 800 n = 20 20

Additional Example 2A: Using Equations to Solve Problems with Percents 35 is 28% of what number? 35 = 28% · n Write an equation. 35 = 0.28 · n Write 28% as a decimal. 35 0.28 0.28 · n 0.28 Divide each side by 0.28 to isolate the variable. = 125 = n 35 is 28% of 125.

Additional Example 2B: Using Equations to Solve Problems with Percents What percent of 9 is 18? 18 = n · 9 Write an equation. 18 9 n · 9 9 Divide each side by 9 to isolate the variable. = 2 = n Write the decimal as a percent. 200% = n 18 is 200% of 9.

Check It Out: Example 2A Solve. 9 is 75% of what number? 9 = 0.75 · n 9 0.75 = 0.75n 12 = n

Check It Out: Example 2B Solve. 24 is 150% of what number? 14 = 1.50 n 24 1.5 1.5n 1.5 = 16 = n

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 = 5.46 Write an equation. Divide both sides by 0.065. x = 84 The price of the shoes with the coupon was $84.

Additional Example 3 Continued Find the price of the shoes without the coupon. 84 + 10 = 94 The 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 = 94 Write an equation. Divide both sides by 0.8. x = 117.5 The original price of the shoes was $117.50.

Check It Out: Example 3A Marie-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 original price of the scarf? Find the price before the sales tax was applied: 1.35 = 0.06 x 1.35 0.06 0.06x 0.06 = $22.50 = x

Check It Out: Example 3A Continued Find the price before Marie used her $5 coupon: 22.50 + 5 = $27.50 Find the price before the markdown: 0.75 · x = 27.50 0.75x 0.75 27.50x 0.75 = x = 36.67 The original price of the scarf was $36.67.

Check It Out: Example 3B In 2008, Brenda made $42,756, which was 105% of what she made in 2007. In 2007, she made $4,000 more than she made in 2006. The amount she made in 2006 was 102% of what she made in 2005. How much did Brenda make in 2005? Find what she made in 2007: 42,756 = 1.05 x 42,756 1.05 1.05x 1.05 = $40,720 = x

Check It Out: Example 3B Continued Find what she made in 2006: 40,720 - $4,000 = $36,720 Find what she made in 2005: 36,720 = 1.02 x 36,720x 1.02 1.02x 1.02 = 36,000 = x Brenda made $36,000 in 2005.

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? n 100 18 225 = Write a proportion. n · 225 = 100 · 18 Set the cross products equal. 225n = 1800 Multiply. 225n 225 1800 225 = Divide each side by 225. n = 8 8% of $225 is $18. The sales tax is 8%.

Check It Out: Example 4A Jarell paid $25.56 for his new bookbag. The amount he paid included a sales tax of $1.56. Find the sales tax rate. n 100 = 1.56 24 30n = 1.56(100) The sales tax rate is 6.5%. Price before sales tax: 25.56 - 1.56 = $24 24n 156 n = 0.065

Check It Out: Example 4B Lisa 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 = 0.055 x The bike cost $200 without sales tax. 11 0.055 = 0.055 x 200 = x

Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

Lesson Quiz Solve. 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? 50 25% 75 1% 6%

Lesson Quiz for Student Response Systems 1. Solve. 19 is 38% of what number? A. 69 B. 50 C. 38 D. 34

Lesson Quiz for Student Response Systems 2. What percent of 170 is 51? A. 25% B. 30% C. 40% D. 50%

Lesson Quiz for Student Response Systems 3. 128% of what number is 96? A. 25 B. 50 C. 75 D. 96

Lesson Quiz for Student Response Systems 4. What percent of 1,520 is 15.2? A. 25% B. 15% C. 10% D. 1%

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%