chapter 6 percent © 2010 pearson education, inc. all rights reserved

Chapter 6

Percent

© 2010 Pearson Education, Inc.All rights reserved.

6.6 Solving Applications Problems with Percent

Objectives

Slide 6.6- 2

1. Find sales tax.

2. Find commissions.

3. Find the discount and sale price.

4. Find the percent of change.

Copyright © 2010 Pearson Education, Inc. All rights reserved.

6- 3

States, counties, and cities often collect taxes on sales to customers. The sales tax is a percent of the total sale. The following formula for finding sales tax is based on the percent equation.


ParallelExample 1

Solving for Sales Tax

Slide 6.6- 4

Sam’s Sporting Goods sells a tent for $189. If the sales tax is 5%, how much tax is paid? What is the total cost of the tent? Use the six problem-solving steps.

Step 1

Step 2

Read the problem. The problem asks for the total cost of the tent including the sales tax.

Work out a plan. Use the sales tax formula to find the amount of sales tax. Add the sales tax to the cost of the item to find the total cost.


ParallelExample 1continued


Slide 6.6- 5


Step 3

Step 4 Solve the problem.

Estimate a reasonable answer. Round $189 to $200. 5% is equivalent to , so divide $200 by 20.

1

20

$200 20 $10 The total estimated cost is $200 + $10 = $210.

part = percent ∙ whole

amount of sales tax rate of tax cost of item Copyright © 2010 Pearson Education, Inc. All rights reserved.



Slide 6.6- 6


Step 4

Step 5 State the answer. The total cost of the tent is $198.45.

a = (5%)($189)

a = (0.05)($189)

a = $9.45Total cost equals $189 + $9.45 = $198.45.

Step 6 Check. The exact answer, $198.45, is close to our estimate of $210.


ParallelExample 2

Finding the Sales Tax Rate

Slide 6.6- 7

The sales tax on a $580 recliner is $46.40. Find the rate of the sales tax.

Step 1

Step 2

Read the problem. The problem asks for the rate of the sales tax.

Work out a plan. Use the sales tax formula.sales tax = rate of tax ∙ cost of item

The cost of the recliner (the whole) is $580, and the amount of sales tax (the part) is $46.40. Use r to represent the unknown rate of tax (the percent).




Slide 6.6- 8


Step 3 Estimate a reasonable answer. Round $580 to $600 and round $46.40 to $50.The sales tax is or So divide 1 by 12 to estimate the percent (rate) of sales tax.

50

600

1.

12

10.83 8%

12




Slide 6.6- 9



sales tax = rate of tax ∙ cost of item

$46.40 = r ∙ $580

46.40 580

580 580

r

0.08 r0.08 is 8%

Step 5 State the answer. The sales tax rate is 8%.

Step 6 Check. The exact answer and the estimate of 8% are the same.

1

1


6- 10

Many salespeople are paid by commission rather than an hourly wage. If you are paid by commission, you are paid a certain percent of your total sales dollars. The formula below for finding the commission is based on the percent equation.


ParallelExample 3

Determining the Amount of Commission

Slide 6.6- 11

Caleb Martinez had exercise equipment sales of $12,700 while working part-time last month. If his commission rate is 9%, find the amount of his commission.

Step 1

Step 2

Read the problem. The problem asks for the amount of commission that Martinez earned.

Work out a plan. Use the commission formula.

Step 3 Estimate a reasonable answer. Round the commission rate to 10% and the sales to $10,000. $10,000 ÷ 10 = $1000




Slide 6.6- 12



Amount of commission = rate of commission ∙ amount of sales

c = (9%)($12,700)

c = (0.09)($12,700)

c = $1143.00




Slide 6.6- 13


Step 5 State the answer. Martinez earned a commission of $1143 for selling the exercise equipment.

Step 6 Check. The exact answer, $1143, is close to the estimate of $1000.


6- 14

A store will reduce prices, or discount, to attract additional customers. Use the following formula to find the discount and the sale price.


ParallelExample 5

Finding a Sale Price

Slide 6.6- 15

Art Designs has a painting with an original price of $620 on sale for 15% off. Find the sale price of the painting.

Step 1

Step 2

Read the problem. The problem asks for the sale price of the painting after a discount of 15%.

Work out a plan. First find the amount of discount by multiplying the original price by the rate of discount. Then, subtract the discount from the original price.




Slide 6.6- 16


Step 3 Estimate a reasonable answer. Round the original price to $600 and the rate of discount from 15% to 20%. Since 20% is equivalent to 1/5, the estimated discount is $600 ÷ 5 = $120. So the estimated sale price is $600 − $120 = $480.




Slide 6.6- 17

Step 4

Step 5

Solve the problem. Amount of discount = rate of discount ∙ original price

a = (0.15)($620)a = $93

State the answer. The sale price of the painting is $527.

Step 6 Check. The exact answer, $527, is close to the estimate of $480.


Sale price = original price − amount of discount

$620 − $93 = $527


6- 18

We are often interested in looking at increases or decreases in sales, production, population, and many other items. Use the following steps to find the percent of increase.


Finding the Percent of Increase

Step 1 Use subtraction to find the amount of increase.

Step 2 Use the percent proportion to find the percent of increase.

amount of increase (part) percent

original value (whole) 100

ParallelExample 6


Slide 6.6- 19

A budget had an increase from $19,600 last year to $40,060 this year. Find the percent of increase.

Step 1

Step 2

Read the problem. The problem asks for the percent of increase.

Work out a plan. Subtract the last year’s budget from this year. Next, use the percent proportion to find the unknown percent.




Slide 6.6- 20

Step 3 Estimate a reasonable answer. Round $19,600 to 20,000 and $40,060 to 40,000. The amount of increase is $40,000 – $20,000 = $20,000. Since the increase is about the same as the original amount, the estimated percent increase is 100%.

A budget had an increase from increased from $19,600 last year to $40,060 this year. Find the percent of increase.




Slide 6.6- 21

Step 4

Step 5

Solve the problem.

State the answer. The percent of increase is about 104%.

Step 6 Check. The exact answer, 104%, is close to the estimate of 100%.

$40,060 − $19,600 = $20,460

A budget had an increase from increased from $19,600 last year to $40,060 this year. Find the percent of increase.

20,460

19,600 100

x

104.4x


6- 22 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Finding the Percent of Decrease

Step 1 Use subtraction to find the amount of decrease.

Step 2 Use the percent proportion to find the percent of decrease.

amount of decrease (part) percent

original value (whole) 100

Copyright © 2010 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

ParallelExample 7


Slide 6.6- 23

The number of minutes Rita used on her cell phone dropped this month to 798 from 840 last month. Find the percent of decease.

Step 1

Step 2

Read the problem. The problem asks for the percent of decrease.

Work out a plan. Subtract the number of minutes this month from last month. Then use the percent proportion.



Slide 6.6- 24

Step 3 Estimate a reasonable answer.



Round 798 to 800 and 840 to 850. So, 850 – 800 = 50. Since 50 is 1/17 of 850, our estimate is 1 ÷ 17 ≈ 0.06 or 6%.



Slide 6.6- 25

Step 4

Step 5

Solve the problem.

State the answer. The percent of decrease in phone minutes was 5%.

Step 6 Check. The exact answer, 5%, is close to the estimate of 6%.

840 − 798 = 4242

840 100

x

5x



chapter 6 percent © 2010 pearson education, inc. all rights reserved

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