Intermediate Algebra (11th edition)

SECTION 2.3 Applications of Linear Equations 67

Evaluate. See Section 1.2.

61.The product of and 5, divided by 1 less than 6

62.Half of added to the reciprocal of

63.The sum of 6 and , multiplied by the additive inverse of 2

64.The product of - 2 and 4, added to the product of - 9 and - 3

- 9

1

• 18, 5

- 3

OBJECTIVES

Applications of Linear Equations

2.3

1 Translate from
words to
mathematical
expressions.

2 Write equations
from given
information.

3 Distinguish between
simplifying
expressions and
solving equations.

4 Use the six steps in
solving an applied
problem.

5 Solve percent
problems.

6 Solve investment
problems.

7 Solve mixture
problems.

OBJECTIVE 1 Translate from words to mathematical expressions.

There are usually key words and phrases in a verbal problem that translate into

mathematical expressions involving addition, subtraction, multiplication, and

division. Translations of some commonly used expressions follow.

PROBLEM-SOLVING HINT

Translating from Words to Mathematical Expressions

Mathematical Expression

Verbal Expression (where x and y are numbers)

Addition

The sumof a number and 7

6 more thana number

3 plusa number

24 added toa number

A number increased by 5

The sumof two numbers

Subtraction

2 less thana number

2 lessa number

12 minusa number

A number decreased by 12

A number subtracted from 10

10 subtracted froma number

The difference betweentwo numbers

Multiplication

16 timesa number

A number multiplied by 6

ofa number (used with fractions x

and percent)

as much asa number x

Twice(2 times) a number 2 x

The productof two numbers xy

Division

The quotientof 8 and a number

A number divided by 13

The ratioof two numbers or the

quotientof two numbers

xy 1 yZ 02

x

13

(^8) x 1 xZ 02
3
4
3
4
2
3
2
3
6 x
16 x
x-y
x- 10
10 - x
x- 12
12 - x
2 - x
x- 2
x+y
x+ 5
x+ 24
3 +x
x+ 6
x+ 7