Solving Percent Problems with Proportions Section 7.3

Solving Percent Problems Solving Percent Problems with Proportionswith Proportions

Section 7.3

To understand the proportion To understand the proportion method, recall that 30% means themethod, recall that 30% means the

ratio of 30 to 100, or .ratio of 30 to 100, or .

30%

Writing Percent Problems as Writing Percent Problems as ProportionsProportions

30100

30100

310

2Martin-Gay, Prealgebra, 5ed

Since the ratio is equal to theSince the ratio is equal to the

ratio , we have the proportionratio , we have the proportion

called the called the percent proportionpercent proportion..

Writing Percent Problems as Writing Percent Problems as Proportions . . .Proportions . . .

,,

301003

1030 3

100 10

3Martin-Gay, Prealgebra, 5ed

always 100

or

percentbase

amount

Percent ProportionPercent Proportion

amount percentbase 100

100a pb

4Martin-Gay, Prealgebra, 5ed

When we translate percent problems to When we translate percent problems to proportions, the proportions, the percentpercent can be can be identified by looking for the symbol % identified by looking for the symbol % or the word or the word percentpercent. The . The basebase usually usually follows the word follows the word ofof. The . The amountamount is the is the part compared to the whole.part compared to the whole.

5Martin-Gay, Prealgebra, 5ed

Helpful HintHelpful Hint

Part of Part of ProportionProportion

How It’s How It’s IdentifiedIdentified

Percent Percent % or percent% or percentBase Base Amount Amount

Appears after Appears after of of

Part compared to Part compared to whole whole

6Martin-Gay, Prealgebra, 5ed

What number is 20% of 8?

amount percent base

amountbase

percent

Solving Percent Proportions for Solving Percent Proportions for the Amountthe Amount

208 100a

7Martin-Gay, Prealgebra, 5ed

20 is 40% of what number?

amount percent base

amountbase

percent

Solving Percent Proportions for Solving Percent Proportions for the Basethe Base

20 40100b

8Martin-Gay, Prealgebra, 5ed

What percent of 40 is 8?

amountpercent base

amountbase

percent

Solving Percent Proportions for Solving Percent Proportions for the Percentthe Percent

840 100

p

Helpful HintHelpful HintRecall from our percent proportion that this number, p already is a percent. Just keep the number the same and attach a % symbol. 9

Helpful HintHelpful Hint

A ratio in a proportion may be simplified A ratio in a proportion may be simplified before solving the proportion. The before solving the proportion. The unknown number in bothunknown number in both

andand

is 20.

6 304 b

3 302 b

10Martin-Gay, Prealgebra, 5ed