Intermediate Algebra (11th edition)

Solving a Mixture Problem When One Ingredient Is Pure

The octane rating of gasoline is a measure of its antiknock qualities. For a standard

fuel, the octane rating is the percent of isooctane. How many liters of pure isooctane

should be mixed with 200 L of 94% isooctane, referred to as 94 octane, to get a mix-

ture that is 98% isooctane?

Step 1 Readthe problem. The problem asks for the amount of pure isooctane.

Step 2 Assign a variable.Let x the number of liters of pure isooctane.

Complete a table. Recall that 100%= 1001 0.01 2 =1.

= 1 100% 2

EXAMPLE 8

74 CHAPTER 2 Linear Equations, Inequalities, and Applications

NOW TRY
EXERCISE 8
How much pure antifreeze
must be mixed with 3 gal of a
30% antifreeze solution to get
a 40% antifreeze solution?

NOW TRY ANSWER

8.^12 gal

Number Percent Liters of Pure

of Liters (as a decimal) Isooctane

x 1 x

200 0.94

x+ 200 0.98 0.98 1 x+ 2002

0.94 12002

Step 3 Write an equation.The equation comes from the last column of the table.

Step 4 Solve. Distributive property

Multiply.

Subtract 0.98xand 188.

Divide by 0.02.

Step 5 State the answer.400 L of isooctane is needed.

Step 6 Checkby showing that 400 +0.94 12002 = 0.98 1400 + 2002 is true.

x= 400

0.02x= 8

x+ 188 = 0.98x+ 196

x+ 0.94 12002 = 0.98x+0.98 12002

x+ 0.94 12002 = 0.98 1 x+ 2002

Complete solution available
on the Video Resources on DVD

2.3 EXERCISES

Concept Check In each of the following, (a)translate as an expression and (b)translate as

an equation or inequality. Use x to represent the number.

1. (a)15 more than a number
   (b)15 is more than a number.
   2. (a)5 greater than a number
   (b)5 is greater than a number.


2. (a)8 less than a number
   (b)8 is less than a number.
   4. (a)6 less than a number
   (b)6 is less than a number.
   5.Concept Check Which one of the following is nota valid translation of “40% of a num-
   ber,” where xrepresents the number?

A.0.40x B.0.4x C. D. 40 x

6.Explain why is nota correct translation of “13 less than a number.”

Translate each verbal phrase into a mathematical expression. Use x to represent the unknown

number. See Example 1.

13 - x

2 x

5

7.Twice a number, decreased by 13 8.The product of 6 and a number, decreased

by 14

9.12 increased by four times a number 10.15 more than one-half of a number

NOW TRY