2-8 Percents Lesson Presentation Lesson Quiz Holt Algebra 1

Objective Solve problems involving percents.

 Example 1A Find 30% of 80. Method 1 Use a proportion. Use the percent proportion. Let x represent the part. 100x = 2400 Find the cross products. Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. x = 24 30% of 80 is 24. Check 30% is the same as , and of 80 is 24. 

Example 1B Find 4% of 36. Method 2 Use an equation. x = 4% of 36 Write an equation. Let x represent the part. x = .04(36) Write the percent as a decimal and multiply. x =1.44 4% of 36 is 1.44.

Example 1C What percent of 45 is 35? Round your answer to the nearest tenth. Method 1 Use a proportion. Use the percent proportion. Let x represent the percent. 45x = 3500 Find the cross products. Since x is multiplied by 45, divide both sides by 45 to undo the multiplication. x ≈ 77.8 35 is about 77.8% of 45.

1D 230 is what percent of 200? Method 2 Use a equation. 230 = x • 200 Write an equation. Let x represent the percent. 230 = 200x Since x is multiplied by 200, divide both sides by 200 to undo the multiplication. 1.15 = x The answer is a decimal. 115% = x Write the decimal as a percent. This answer is reasonable; 230 is more than 100% of 200. 230 is 115% of 200.

1E 20 is 0.4% of what number? Method 2 Use an equation. Write an equation. Let x represent the whole. 20 = 0.4% of x 20 = 0.004 • x Write the percent as a decimal. Since x is multiplied by 0.004, divide both sides by 0.004 to undo the multiplication. 5000 = x 20 is 0.4% of 5000.

Example 2A: Application The serving size of a popular orange drink is 12 oz. The drink is advertised as containing 5% orange juice. How many ounces of orange juice are in one serving size? Use the percent proportion. Let x represent the percent. 100x = 60 Since x is multiplied by 100, divide both sides by 100 to undo the multiplication. x = 0.6 A 12 oz orange drink contains 0.6 oz of orange juice.

Example 2B A telemarketer earns $350 per week plus 12% commission on sales. Find her total pay for a week in which her sales were $940. total pay = base salary + commission Write the formula for total pay. = base + % of total sales Write the formula for commission. = 350 + 12% of 940 Substitute values given in the problem. = 350 + (0.12)(940) Write the percent as a decimal. = 350 + 112.80 Multiply. = 462.80 Add. The telemarketer’s total pay was $462.80.

Example 2C Lunch at a restaurant is $27.88. Estimate a 15% tip and determine the total bill. Step 1 First round $27.88 to $30. Step 2 Think: 15% = 10% + 5% 10% of $30 = $3.00 Move the decimal point one place left. Step 3 Think 5% = 10% ÷ 2 = $3.00 ÷ 2 = $1.50 Step 4 15 = 10% + 5% = $3.00 + $1.50 = $4.50 The tip should be about $4.50. Total bill is $32.38

Example 2D The sales tax rate is 7.25%. Estimate the sales tax on a book that costs $19.97. Step 1 First round 7.25% to 7% and $19.97 to $20. Move the decimal point two places left. Step 2 Think: 7% = 7(1%) 1% of $20 =$0.20 Step 3 7% = 7(1%) = 7($0.20) = $1.40 The sales tax is about $1.40.

Example 3A: Discounts A student paid $31.20 for art supplies that normally cost $52.00. Find the percent discount . Think: 20.80 is what percent of 52.00? Let x represent the percent. $52.00 – $31.20 = $20.80 20.80 = x(52.00) Since x is multiplied by 52.00, divide both sides by 52.00 to undo the multiplication. 0.40 = x 40% = x Write the answer as a percent. The discount is 40%

Example 3B A $220 bicycle was on sale for 60% off. Find the sale price. Method 2 Subtract the percent discount from 100%. 100% – 60% = 40% The bicycle was 60% off of 100% . 0.40(220) = 88 Find 40% of 220. This is the discount from the original price. 220 – 88 = 142 By this method, the discount is $88. The sale price is $142.00.