6.3 – Percent Problems with Equations

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6.3 – Percent Problems with Equations. Translate the following statements to equations:. 8 is what percent of 48?. 2.6 is 40% of what number?. What number is 90% of 0.045?. 6.3 – Percent Problems with Equations. Write the equation and solve. What number is 25% of 90?. x. =. 25%. 90.

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## 6.3 – Percent Problems with Equations

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6.3 – Percent Problems with Equations

Translate the following statements to equations:

8 is what percent of 48?

2.6 is 40% of what number?

What number is 90% of 0.045?

6.3 – Percent Problems with Equations

Write the equation and solve.

What number is 25% of 90?

x

=

25%

90

.

x

=

0.25

90

.

x

=

22.5

6.3 – Percent Problems with Equations

Write the equation and solve.

15% of what number is 2.4?

x

=

15%

2.4

.

0.15

x

=

2.4

0.15

x

=

2.4

0.15

0.15

x

=

16

6.3 – Percent Problems with Equations

Write the equation and solve.

What percent of 90 is 27?

x

=

90

27

.

=

90x

27

90

x

=

27

90

90

x

=

0.3

x

=

100%

0.3

.

x

=

30%

6.3 – Percent Problems with Equations

Write the equation and solve.

18 is 4.5% of what number?

x

18

=

4.5%

.

18

0.045x

=

=

0.045x

18

0.045

0.045

x

400

=

6.5 – Applications of Percent

The length of the Appalachian Trail is 2174 miles. Twenty-five percent of the length is in the state of Virginia. How many miles are in Virginia?

x

2174

25%

=

.

2174 . 0.25

=

x

543.5

=

x

miles

6.5 – Applications of Percent

There are currently 130,000 nurses in the state of Florida. Of those nurses, 34,000 are new. What is the percentage of new nurses? Round to the nearest whole percent.

x

34,000

130,000

=

.

130,000 x

=

34,000

130,000

130,000

x

=

0.261

x

=

0.261 . 100%

x

=

26.1%

x

=

26%

6.5 – Applications of Percent

In 2000, there were 240 million vehicles on the road in the United States. In seven years, the total was increased by 3%. (a) What was the increase in the number of vehicles in the seven years? (b) What was the total number of vehicles in 2007?

x

=

(a)

3%

7.2

+

(b)

240

240

.

x

240

0.03

=

.

247.2

million vehicles

x

=

7.2

million vehicles

6.5 – Applications of Percent

Percent of Increase:

amount of increase

100%

.

original amount

The number of people attending a local play increased from 285 on Friday to 333 on Saturday. Find the percent of increase and round to the nearest tenth percent.

48

333 – 285 =

amount of increase:

285

original amount:

48

16.84%

=

16.8%

100%

=

0.1684

100%

=

.

.

285

increase

6.5 – Applications of Percent

Percent of Decrease:

amount of decrease

100%

.

original amount

A town with a population of 20,200 in 1995 decreased to 18,483 in 2005. What is the percent decrease? Round to the nearest tenth percent, if necessary

20,200 – 18483 =

amount of decrease:

1717

20,200

original amount:

1717

decrease

8.5%

100%

=

0.085

100%

=

.

.

20,200

6.6 – Percent and Problem Solving: Sales Tax, Commission, and Discounts

Sales Tax and Total Price:

Sales Tax

=

purchase price

tax rate as a decimal

.

purchase price: \$21.00

tax rate: 7%

= 0.07

Sales Tax = \$21.00 . 0.07

Sales Tax = \$1.47

sales tax

=

Total Price

purchase price

+

Total Price = \$21.00 + \$1.47

Total Price = \$22.47

6.6 – Percent and Problem Solving: Sales Tax, Commission, and Discounts

An artificial holiday tree costs \$59.90. If the tax rate is 8.5%, what are the sales tax and the total price. Round the sales tax to the nearest cent.

Total Price

Sales Tax

8.5%

59.90 + 5.09

59.90

.

64.99

59.90

0.085

.

\$64.99

5.0915

\$5.09

6.6 – Percent and Problem Solving: Sales Tax, Commission, and Discounts

If a car costs \$18,500 and the sales tax is \$1665, what is the sales tax rate?

x

=

18500

1665

.

18500 x = 1665

18500

18500

x

=

0.09

x

100%

=

0.09

.

x

=

9%

6.6 – Percent and Problem Solving: Sales Tax, Commission, and Discounts

commission rate as a decimal

Commission

=

total sales

.

Total sales: \$500.00

Commission rate: 15%

= 0.15

Commission = 500.00 . 0.15

Commission = \$75.00

6.6 – Percent and Problem Solving: Sales Tax, Commission, and Discounts

A sales representative from a paper products company sold \$47,632 worth of products during a month. The sales commission rate was 6.6%. What was the commission?

Commission

6.6%

47,632

.

0.066

47,632

.

3143.712

\$3,143.71

6.6 – Percent and Problem Solving: Sales Tax, Commission, and Discounts

A salesperson earns \$645 for selling \$4300 worth of appliances. What is the commission rate?

x

=

645

4,300

.

4,300 x = 645

4,300

4,300

x

0.15

=

100%

x

0.15

=

.

x =

15%

6.6 – Percent and Problem Solving: Sales Tax, Commission, and Discounts

Discount and Sales Price:

Amount of Discount

=

original price

discount rate as a decimal

.

original price: \$160.00

discount rate: 28%

= 0.28

Amount of discount = \$160.00 . 0.28

Amount of discount= \$44.80

amount of discount

original price

Sales Price

=

Sales Price = 160.00 – 44.8

Sales Price = \$115.20

6.6 – Percent and Problem Solving: Sales Tax, Commission, and Discounts

A discontinued washer/dryer combination is advertise on sale for 35% off the original price of \$700. What are the amount of discount and the sales price?

Sales Price

Amount of discount

700.00 – 245.00

35%

700

.

455.00

700

0.35

.

\$455.00

245.00

\$245.00