Beginning Algebra, 11th Edition

Using Percents to Find Percentages

(a)If a chemist has 40 L of a 35% acid solution, then the amount of pure acid in the

solution is

40 L 0.35 14 L.

Amount of solution Rate of concentration Amount of pure acid

(b)If $1300 is invested for one year at 7% simple interest, the amount of interest

earned in the year is

$1300 0.07 $91.

Principal Interest rate Interest earned NOW TRY

* =

* =

EXAMPLE 1

140 CHAPTER 2 Linear Equations and Inequalities in One Variable

Write 35% as a decimal.

Using a table helps organize the information in a problem and more easily set

up an equation, which is usually the most difficult step.

PROBLEM-SOLVING HINT

Solving a Mixture Problem

A chemist needs to mix 20 L of a 40% acid solution with some 70% acid solution to

obtain a mixture that is 50% acid. How many liters of the 70% acid solution should

be used?

Step 1 Readthe problem. Note the percent of each solution and of the mixture.

Step 2 Assign a variable.

Let the number of liters of 70% acid solution needed.

Recall from Example 1(a)that the amount of pure acid in this solution is the

product of the percent of strength and the number of liters of solution, or

0.70x. Liters of pure acid in xliters of 70% solution

The amount of pure acid in the 20 L of 40% solution is

Liters of pure acid in the 40% solution

The new solution will contain of 50% solution. The amount

of pure acid in this solution is

Liters of pure acid in the 50% solution

FIGURE 15illustrates this information, which is summarized in the table.

0.50 1 x+ 202.

1 x+ 202 liters

0.40 1202 =8.

x=

EXAMPLE 2

Unknown number

of liters, x

20 L (x + 20) liters

50%

from 40%

from 70% from 40% from 70%

After mixing

+=

FIGURE 15

Liters of Rate Liters of

Solution (as a decimal) Pure Acid

x 0.70 0.70x

20 0.40

x+ 20 0.50 0.50 1 x+ 202

0.40 1202 = 8

NOW TRY

EXERCISE 1

(a)How much pure alcohol

is in 70 L of a 20%

alcohol solution?

(b)Find the annual simple

interest if $3200 is

invested at 2%.

NOW TRY ANSWERS

1. (a)14 L (b)$64

OBJECTIVE 2 Solve problems involving mixtures.

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