Basic Mathematics for College Students

5.2 Proportions 437

1 inch corresponds to6 feet as4.5 inches corresponds towfeet.

SolveTo find the actual wingspan of the airplane, we solve the proportion for w.

Set the cross products equal to form an equation.

To simplify each side of the equation, do the multiplication.

State The actual wingspan of the plane is 27 feet.

CheckEvery 1 inch on the scale drawing corresponds to an actual length of 6 feet
on the plane. Therefore, a 5-inch measurement corresponds to an actual wingspan
of , or 30 feet. It seems reasonable that a 4.5-inch measurement
corresponds to an actual wingspan of 27 feet.

5 6 feet

w 27

1 w 6 4.5

Measure on the drawing

 Measure on the plane

1 

6



4.5

 w

Measure on the drawing 

Measure on the plane

EXAMPLE (^11) Baking A recipe for chocolate cake calls for cups of
sugar for every cups of flour. If a baker has only cup of sugar on hand, how
much flour should he add to it to make chocolate cake batter?
Analyze

• The rate of cups of sugar for every cups of flour can be expressed as:


• How much flour should be added to cups of sugar?

Form We will let the variable frepresent the unknown cups of flour. If we
compare the cups of sugar to the cups of flour, we know that the two rates must be
equal and we can write a proportion.

cups of sugar is to cups of flour as cup of sugar is tofcups of flour

SolveTo find the amount of flour that is needed, we solve the proportion for f.

This is the proportion to solve.

Set the cross products equal to each other to form an equation.

Write each mixed number as an improper fraction.

To undo the multiplication by and isolate^32 f, divide both sides by.^32

3

2

f

3

2



9

4



1

2

3

2

3

2

f

9

4



1

2

1

1

2

f 2

1

4



1

2

1

1

2

2

1

4



1

2

f

Cup of sugar

 Cups of flour

11 

2

2

1

4



1

2

 f

Cups of sugar 

Cups of flour

1

2

2

1

4

1

1

2

3

4

1

1

2

cups sugar

2

1

4

cups flour

(^1122 14)
(^2 14 12)
(^1 12)
Self Check 11
BAKINGSee Example 11. How
many cups of flour will be needed
to make several chocolate cakes
that will require a total of
cups of sugar?
Now TryProblem 89
(^1212)
4
3
.5
 6
27.0