Basic Mathematics for College Students

434 Chapter 5 Ratio, Proportion, and Measurement

Self Check 7

Solve the proportion:

Now TryProblem 45

6.7

x



33.5

38

EXAMPLE 7

Solve the proportion:

StrategyWe will set the cross products equal to each other to form an equation.

WHYThen we can isolate the variable xon one side of the equation to find the

unknown term that it represents.

Solution

This is the proportion to solve.

Thus,xis 7.7. Check the result in the original proportion.

To simplify the left side of the equation,

do the division: 55.44 7.2 7.7.

To simplify the right side, remove the common factor of 7.2.

7.7x

To undo the multiplication by 7.2 and

(^) isolate x, divide both sides by 7.2.

55.44

7.2



7.2#x

7.2

To simplify the left side of the equation,

55.447.2 multiply: 3.5 15.84 55.44.

#x

Set the cross products equal to each

3.515.847.2x other to form an equation.

3.5

7.2



x

15.84

3.5

7.2



x

15.84

EXAMPLE 8

Solve the proportion. Write the result as a mixed number.

StrategyWe will set the cross products equal to each other to form an equation.

WHYThen we can isolate the variable xon one side of the equation to find the

unknown term that it represents.

Solution

This is the proportion to solve.

Write each mixed number as an improper fraction.

To undo the multiplication by and isolate x,

divide both sides by.

To simplify the left side, remove the common factor

of in the numerator and denominator. Perform the

division on the right side indicated by the complex

fraction bar. Multiply the numerator of the complex

fraction by the reciprocal of , which is.

Multiply the numerators.

x Multiply the denominators.

21  11  2

5  2  33

2

33

33

2

33

2

x

21

5



11

2



2

33

33

2

33

2

x

33

2

33

2



21

5



11

2

33

2

x

33

2



21

5



11

2

Set the cross products equal to each

x (^16) other to form an equation.

1

2

 4

1

5

 5

1

2

x

4

1

5



5

1

2

16

1

2

x

4

1

5



5

1

2

16

1

2

Self Check 8

Solve the proportion:

Write the result as a mixed

number.

Now TryProblem 49

x

2

1

3



2

1

4

1

1

2

7.7

7.255.44

50 4

504

 504

0

15.84

 3.5

7920

47520

55.440