UNIT 2.10 CHANGING EXPRESSED UNIT 2.10 CHANGING EXPRESSED

AS A PERCENTAS A PERCENT

Warm Up

1. Write 0.03 as a percent.

2. Write as a decimal. Find each value. Round to the nearest tenthif necessary.3. Find 10% of 53.

Solve for x.

5. 40 = (x) (20)

4. Find of 50.

6. 114 = (36) (x)

3%

0.045

384

5.3 1.25

Use common applications of percents.Estimate with percents.

Objectives

commissioninterestsales taxprincipaltip

Vocabulary

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.

Write the formula for total pay.total pay = base salary + commission Write the formula for commission.

Substitute values given in the problem.= 26,000 + 5% of 300,000= base + % of total sales

Write the percent as a decimal.= 26,000 + (0.05)(300,000)Multiply.= 26,000 + 15,000Add.= 41,000

Mr. Cortez’s total pay was $41,000.

Write the formula for total pay.total pay = base salary + commission Write the formula for commission.

Substitute values given in the problem.= 350 + 12% of 940= base + % of total sales

Write the percent as a decimal.= 350 + (0.12)(940)Multiply.= 350 + 112.80Add.= 462.80

The telemarketer’s total pay was $462.80.

A telemarketer earns $350 per week plus 12% commission on sales. Find her total pay for a week in which her sales were $940.

Check It Out! Example 1

Interest is the amount of money charged for borrowing money, or the amount of money earned when saving or investing money. Principal is the amount borrowed or invested. Simple interest is interest paid only on the principal.

Simple Interest Paid Annually

Time in years

Interest rate peryear as a decimal

Principal

Simple interest

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

The amount of interest is $862.50.

Multiply.

Example 2B: Financial Application

After 6 months, the simple interest earned on an investment of $5000 was $45. Find the interest rate.

I = Prt Write the formula for simple interest.

45 = 2500r

0.018 = rThe interest rate is 1.8%.

Substitute the given values.

Multiply 5000 .. Since r is

multiplied by 2500, divide

both sides by 2500 to undo

the multiplication.

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 2aFind the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually.

I = Prt Write the formula for simple interest.

I = 270

The interest earned is $270.

Substitute the given values.

Multiply.

I = (3000)(0.045)(2)

Check It Out! Example 2bThe simple interest paid on a loan after 6 months was $306. The annual interest rate was 8%. Find the principal.

I = Prt Write the formula for simple interest.

The remaining principal is $7650.

Substitute the given values. 306 = (P)(0.08)

306 =.04P

7650 = P

Multiply 0.08 . Since P is

multiplied by 0.04 , divide

both sides by 0.04.

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

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.

Move the decimal point one place left.

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.

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.

Move the decimal point two places left.

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

Check It Out! Example 3aEstimate a 15% tip on a check for $21.98.

Step 1 Think: 15% = 10% + 5% 10% of $22 = $2.20

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.

Move the decimal point one place left.

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

Step 3 8% = 8(1%) = 8($0.70) = $5.60

The sales tax is about $5.60.

Check It Out! Example 3b

Move the decimal point two places left.

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

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