7-8 Solving Percents Problems I CAN determine the percent given the part and the whole. I CAN determine the whole given the percent and the part.

7-8 Solving Percents Problems 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.

7-8 Solving Percents Problems Proportion Method Equation Method n 100 = Part Whole Part Whole What percent of 24 is 16.5? n · 24 = 100 · n = 1,650 n = n · 24 = 16.5 n = n = 68.75% Sloths spend about 69% of the day sleeping!

7-8 Solving Percents Problems Solve. Example 1: Using Proportions to Solve Problems with Percents A. What percent of 40 is 25? n 100 = n · 40 = 100 · 25 40n = 2,500 40n 40 = 2, n = 62.5% Write a proportion. Set the cross products equal. Multiply. Divide each side by 40 to undo the multiplication.

7-8 Solving Percents Problems Solve. Example 1: Using Proportions to Solve Problems with Percents B. 15 is 25% of what number? = 15 n n · 25 = 100 · 15 25n = 1,500 25n 25 = 1, n = 60 Write a proportion. Set the cross products equal. Multiply. Divide each side by 25 to undo the multiplication.

7-8 Solving Percents Problems Solve. You Try! Example 1 A. What percent of 50 is 10? n 100 = n · 50 = 100 · 10 50n = 1,000 50n 50 = 1, n = 20% Write a proportion. Set the cross products equal. Multiply. Divide each side by 50 to undo the multiplication.

7-8 Solving Percents Problems Solve. You Try! Example 1 B. 8 is 40% of what number? = 8n8n n · 40 = 100 · 8 40n = n 40 = n = 20 Write a proportion. Set the cross products equal. Multiply. Divide each side by 40 to undo the multiplication.

7-8 Solving Percents Problems Solve. Example 2: Using Equations to Solve Problems with Percents A. 35 is 28% of what number? 35 = 28% · n 35 = 0.28 · n = 0.28 · n 0.28 n = 125 Write an equation. Write 28% as a decimal. Divide each side by 0.28 to undo the multiplication.

7-8 Solving Percents Problems Solve. Example 2: Using Equations to Solve Problems with Percents B. What percent of 9 is 18? n · 9 = 18 n · 9 9 = 18 9 n = 2 n = 200% Write an equation. Divide each side by 9 to undo the multiplication. Write the decimal as a percent.

7-8 Solving Percents Problems Solve. You Try! Example 2 A. 36 is 24% of what number? 36 = 24% · n 36 = 0.24 · n n = 150 Write an equation. Write 24% as a decimal. Divide each side by 0.24 to undo the multiplication = 0.24 · n 0.24

7-8 Solving Percents Problems Solve. You Try! Example 2 B. What percent of 6 is 36? n · 6 = 36 n · 6 6 = 36 6 n = 6 n = 600% Write an equation. Divide each side by 6 to undo the multiplication. Write the decimal as a percent.

7-8 Solving Percents Problems A portable DVD player costs $225 before tax at an appliance warehouse. What is the sales tax rate if the tax is $18? Example 3: Finding Sales Tax n 100 = n · 225 = 100 · 18 8% of $225 is $18. The sales tax is 8%. Write a proportion. Set the cross products equal. Multiply. Restate the question: What percent of $225 is $18? 225n = n 225 = Divide each side by 225. n = 8

7-8 Solving Percents Problems A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56? You Try! Example 3 n 100 = n · 800 = 100 · 56 7% of $800 is $56. The sales tax is 7%. Write a proportion. Set the cross products equal. Multiply. Restate the question: What percent of $800 is $56? 800n = n 800 = Divide each side by 800. n = 7

7-8 Solving Percents Problems CAN YOU determine the percent given the part and the whole? CAN YOU determine the whole given the percent and the part?

7-8 Solving Percents Problems Lesson Quiz Solve is 42% of what number? 2. What percent of 292 is 73? % 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? 25% % 6%

7-8 Solving Percents Problems HOMEWORK p. 324: 1-9 odd, even