Applications of Percents 2-9 Applications of Percents Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

Warm Up 1. Write 0.03 as a percent. 2. Write as a decimal. Find each value. Round to the nearest tenth if necessary. 3. Find 10% of 53. Solve for x. 5. 40 = (x) (20) 3% 0.045 4. Find of 50. 5.3 1.25 6. 114 = (36) (x) 4 38

Objectives Use common applications of percents. Estimate with percents.

Vocabulary commission interest sales tax Principle tip

A commission is money paid to a person or a company for making a sale A commission is money paid to a person or a company for making a sale. Usually the commission is a percent of the sale amount.

Caution! You must convert a percent to a decimal or a fraction before doing any calculations with it.

Example 1: Business Application Mr. Cortez earns a base salary of $26,000 plus a sales commission of 5%. His total sales for one year were $300,000. Find his total pay for the year. total pay = base salary + commission Write the formula for total pay. = base + % of total sales Write the formula for commission. = 26,000 + 5% of 300,000 Substitute values given in the problem. = 26,000 + (0.05)(300,000) Write the percent as a decimal. = 26,000 + 15,000 Multiply. = 41,000 Add. Mr. Cortez’s total pay was $41,000.

Check It Out! Example 1 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.

I = P r t Simple Interest Paid Annually Interest is the amount of money charged for borrowing money, or the amount of money earned when saving or investing money. Principle is the amount borrowed or invested. Simple interest is interest paid only on the principle. Simple Interest Paid Annually I = P r t Simple interest Time in years Principle Interest rate per year as a decimal

Example 2A: Financial Application Find the simple interest paid for 3 years on a $2500 loan at 11.5% per year. I = Prt Write the formula for simple interest. I = (2500)(0.115)(3) Substitute known values. Write the interest rate as a decimal. I = 862.50 Multiply. The amount of interest is $862.50.

Example 2B: Financial Application After 6 months, the simple interest earned on an investment of $5000 was $45. Find the interest rate. Write the formula for simple interest. I = Prt Substitute the given values. Multiply 5000 .. Since r is multiplied by 2500, divide both sides by 2500 to undo the multiplication. 45 = 2500r 0.018 = r The interest rate is 1.8%.

Helpful Hint When you are using the formula I= Prt to find simple interest paid annually, t represents time in years. One month is year.

Check It Out! Example 2a Find the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually. Write the formula for simple interest. I = Prt I = (3000)(0.045)(2) Substitute the given values. Multiply. I = 270 The interest earned is $270.

Check It Out! Example 2b The simple interest paid on a loan after 6 months was $306. The annual interest rate was 8%. Find the principle. Write the formula for simple interest. I = Prt 306 = (P)(0.08) Substitute the given values. Multiply 0.08 . Since P is multiplied by 0.04 , divide both sides by 0.04. 306 =.04P 7650 = P The remaining principle is $7650.

A tip is an amount of money added to a bill for service A tip is an amount of money added to a bill for service. it is usually a percent of the bill before sales tax is added. Sales tax is a percent of an item’s cost.

Sales tax and tips are sometimes estimated instead of calculated exactly. When estimating percents, use percents that you can calculate mentally. Find 10% of a number by moving the decimal point one place to the left. Find 1% of a number by moving the decimal point two places to the left. Find 5% of a number by finding of 10% of the number.

Example 3A: Estimating with Percents Lunch at a restaurant is $27.88. Estimate a 15% tip. 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.

Example 3B: Estimating with Percents 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.

Helpful Hint A 6.25% sales tax rate means that for every $100 you spend, you would pay $6.25 in sales tax.

Check It Out! Example 3a Estimate a 15% tip on a check for $21.98. Step 1 Think: 15% = 10% + 5% 10% of $22 = $2.20 Move the decimal point one place left. Step 2 Think 5% = 10% ÷ 2 $2.20 ÷ 2 = $1.10 Step 3 15% = 10% +5% = $2.20 + $1.10 = $3.30 The tip should be about $3.30.

Check It Out! Example 3b Estimate the tax on shoes that cost $68.50 when the sales tax rate is 8.25%. Step 1 First round 8.25% to 8% and $68.50 to $70. Step 2 Think: 8% = 8(1%) 1% of $70 =$0.70 Move the decimal point two places left. Step 3 8% = 8(1%) = 8($0.70) = $5.60 The sales tax is about $5.60.

Lesson Quiz: Part 1 1. A computer salesperson earns a base salary of $32,000 per year plus a commission of 6% on total sales. Total sales for one year were $350,000. Find the salesperson’s total pay for the year. $53,000 2. Find the simple interest paid for 9 months on a a $500 loan at 8% per year. $30 3. After 2 years the simple interest earned on an investment of 4000 was $216. Find the interest rate. 2.7%

Lesson Quiz: Part 2 4. A family’s dinner check was $38.82. Estimate a 15% tip. About $6.00 5.The sales tax rate is 7.1%. Estimate the sales tax on a television set that costs $399. About $28