7 8 Solving Percents Problems Learn to solve

7 -8 Solving Percents Problems Learn to solve problems involving percents.

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 Part Whole n = 16. 5 24 100 Part Whole n · 24 = 100 · 16. 5 24 n = 1, 650 Equation Method What percent of 24 is 16. 5? n n = 68. 75 Sloths spend about 69% of the day sleeping! · 24 = 16. 5 n = 0. 6875 n = 68. 75%

7 -8 Solving Percents Problems Additional Example 1 A: Using Proportions to Solve Problems with Percents Solve. What percent of 40 is 25? n = 25 Write a proportion. 100 40 n · 40 = 100 · 25 Set the cross products equal. 40 n = 2, 500 Multiply. 40 n = 2, 500 40 40 n = 62. 5 Divide each side by 40 to isolate the variable. 25 is 62. 5% of 40.

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

7 -8 Solving Percents Problems Check It Out: Example 1 A Solve. What percent of 50 is 10? n = 10 Write a proportion. 100 50 n · 50 = 100 · 10 Set the cross products equal. 50 n = 1, 000 Multiply. 50 n = 1, 000 50 50 n = 20 Divide each side by 50 to isolate the variable. 10 is 20% of 50.

7 -8 Solving Percents Problems Check It Out: Example 1 B Solve. 8 is 40% of what number? 40 = 8 100 n n · 40 = 100 · 8 Write a proportion. Set the cross products equal. 40 n = 800 Multiply. 40 n = 800 40 40 n = 20 Divide each side by 40 to isolate the variable. 8 is 40% of 20.

7 -8 Solving Percents Problems Additional Example 2 A: Using Equations to Solve Problems with Percents Solve. 35 is 28% of what number? 35 = 28% · n Write an equation. 35 = 0. 28 · n Write 28% as a decimal. 35 = 0. 28 · n 0. 28 Divide each side by 0. 28 to isolate the variable. 125 = n 35 is 28% of 125.

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

7 -8 Solving Percents Problems Check It Out: Example 2 A Solve. 36 is 24% of what number? 36 = 24% · n Write an equation. 36 = 0. 24 · n Write 24% as a decimal. 36 = 0. 24 · n 0. 24 Divide each side by 0. 24 to isolate the variable. 150 = n 36 is 24% of 150.

7 -8 Solving Percents Problems Check It Out: Example 2 B Solve. What percent of 6 is 36? 36 = n · 6 6 6 6=n Write an equation. Divide each side by 6 to isolate the variable. Write the decimal as a percent. 600% = n 36 is 600% of 6.

7 -8 Solving Percents Problems Additional Example 3: 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 = 18 Write a proportion. 100 225 n · 225 = 100 · 18 Set the cross products equal. 225 n = 1800 Multiply. 225 n = 1800 225 Divide each side by 225. n=8 8% of $225 is $18. The sales tax is 8%.

7 -8 Solving Percents Problems Check It Out: Example 3 A new flat screen TV costs $800 before tax at an appliance warehouse. What is the sales tax rate if the tax is $56? Restate the question: What percent of $800 is $56? n = 56 Write a proportion. 100 800 n · 800 = 100 · 56 Set the cross products equal. 800 n = 5600 Multiply. 800 n = 5600 800 Divide each side by 800. n=7 7% of $800 is $56. The sales tax is 7%.