Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 1.

Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 1


Equations, Inequalities, and Applications

Chapter 2


2.6

Ratio, Proportion, and Percent


Objectives

1. Write ratios.2. Solve proportions.3. Solve applied problems using proportions.4. Find percentages and percents.

2.6 Ratio, Proportion, and Percent


Writing Ratios

Ratio

A ratio is a comparison of two quantities using a quotient.

The ratio of the number a to the number b is written

a to b, a : b, or .

ab



(a) The ratio of 7 yards to 4 yards is

Writing Ratios

(b) To find the ratio of 8 feet to 6 yards, first convert 6 yards to feet.

74

7 yd4 yd

= .

6 yards = 6 • 3 = 18 ft

49

8 ft18 ft

= .8 ft6 yd

=

The ratio of 8 feet to 6 yards is thus

Example 1 Write a ratio for each word phrase.



Size Price

18-oz $1.89

40-oz $4.16

64-oz $7.04

Writing Ratios

Example 2 What size is the best buy? That is, which size has the lowest unit price?

PEANUT BUTTER



Writing Ratios

Example 2 (continued)

Size Price Unit Cost (dollars per ounce)

18-oz $1.89

40-oz $4.16

64-oz $7.04

$1.8918

$4.1640

$7.0464

= $0.105

= $0.104

= $0.110

Best Buy!

Because the 40-oz size produces the lowest unit cost, it is the best buy.



Solving Proportions

ab

cd

=If , then ad and bc are equal and are called cross

products.

A proportion says that two ratios are equal, so it is a special type of equation. We read the proportion

ab

cd

= (b, d ≠ 0).

as “a is to b as c is to d.” We can also find the products ad and bc by multiplying diagonally.



Solving Proportions

Cross products must be equal.

Example 3 Solve the proportion.

23

x51=

23

x51=

2 • 51 = 3 • x

Multiply.102 = 3x

Divide by 3.34 = x

Check by substituting 34 for x in the proportion. The solution is 34.



Solving Proportions

Cross products must be equal.6 ( w – 4 ) = 3 ( w + 1 )

3w = 27

Divide by 3.w = 9

Check that the solution is 9.

Example 4Solve the equation. =

w – 43

w + 16

=w – 43

w + 16

6w – 24 = 3w + 3 Distribute.

Add 24.6w = 3w + 27

Subtract 3w.



Solving Applied Problems Using Proportions

Cross products must be equal.15.33x = 7.0(35.04)

He pumped a total of 16 gal. Check this answer. Notice that the way the proportion is set up uses the fact that the unit price is the same, no matter how the gallons are purchased.

=$15.337.0

$35.04x

15.33x = 245.28 Multiply.

Divide.x = 16

Example 5 After Edwin pumped 7.0 gal of gasoline, the display showing the price read $15.33. When he finished pumping the gasoline, the display read $35.04. How many gallons did he pump?

Price PriceGallons Gallons



Finding Percentages and Percents

We can solve a percent problem by writing it as a proportion

ab

P100

=

The amount, or percentage, is compared to the base (the whole amount). Since percent means per 100, we compare the numerical value of the percent to 100.

amountbase

percent100

= or .




Cross products must be equal.100a = 750(16)

Thus, 16% of 750 is 120.

100a = 12,000 Multiply.

Divide.a = 120

Example 6 Find 16% of 750.

ab

P100

=

a750

16100

=




Cross products must be equal.100a = 15(26)

The amount of the discount on the CD is $3.90, and the sale price is $15.00 – $3.90 = $11.10.

100a = 390 Multiply.

Divide.a = 3.90

Example 7 A CD with a regular price of $15 is on sale this week at 26% off. Find the amount of the discount and the sale price this week.

ab

P100

=

a15

26100

=




Cross products must be equal.100(255) = 850P

The sale price represented a 30% savings.

25,500 = 850P Multiply.

Divide.30 = P

Example 8 A computer advertisement was listed in the newspaper for $595. The regular price was $850. What percent of the regular price was the savings?

ab

P100

=

255850

P100

=The savings amounted to $850 – $595 = $255.


Copyright © 2010 Pearson Education, Inc. All rights reserved. 2.6 – Slide 1.

Documents