Basic Mathematics for College Students

Write proportions to solve application problems.

Proportions can be used to solve application problems from a wide variety of fields
such as medicine, accounting, construction, and business. It is easy to spot problems
that can be solved using a proportion. You will be given a ratio (or rate) and asked to
find the missing part of another ratio (or rate). It is helpful to follow the five-step
problem-solving strategy seen earlier in the text to solve proportion problems.

4

5.2 Proportions 435

Write the improper fraction as a mixed number.

Thus,xis 1. Check this result in the original proportion.

2

5

x 1

2

5

Multiply the remaining factors in the numerator.

x Multiply the remaining factors in the denominator.

7

5

To simplify the fraction, factor 21 and 33,

and then remove the common factors 2, 3,

and 11 in the numerator and denominator.

x

3

1

 7  11

1

 2

1

5  2

1

 3

1

 11

1

Using Your CALCULATOR Solving Proportions with a Calculator

To solve the proportion in Example 7, we set the cross products equal and

divided both sides by 7.2 to isolate the variable x.

We can find xby entering these numbers and pressing these keys on a calculator.

3.5 15.84 7.2

On some calculators, the key is pressed to find the result.

Thus,xis 7.7.

ENTER

   7.7

3.515.84

7.2

x

EXAMPLE (^9) Shopping If 5 apples cost $1.15, find the cost of 16 apples.
Analyze

• We can express the fact that 5 apples cost $1.15 using the rate:.


• What is the cost of 16 apples?

Form We will let the variable crepresent the unknown cost of 16 apples. If we
compare the number of apples to their cost, we know that the two rates must be
equal and we can write a proportion.

5 apples isto $1.15 16 apples isto $c.

SolveTo find the cost of 16 apples, we solve the proportion for c.

Set the cross products equal to

each other to form an equation.

To simplify the right side of the equation,

multiply: 1.15(16) 18.4.

To simplify the left side, remove the common factor of 5.

On the right side, do the division: 18.4 5 3.68.

c3.68

To undo the multiplication by 5 and

(^) isolate c,divide both sides by 5.
5 #c
5



18.4

5

5 #c18.4

5 c1.15 16

The units can be written

outside of the proportion.

16 apples

 Cost of 16 apples

5 

1.15



16

 c

5 apples 

Cost of 5 apples

5 apples

$1.15

Self Check 9

CONCERT TICKETSIf 9 tickets to a

concert cost $112.50, find the cost

of 15 tickets.

Now TryProblem 73

3.68

5 18.40

 15

34

 30

40

 40

0