Basic Mathematics for College Students

Self Check 10

SCALE MODELSIn a scale model

of a city, a 300-foot-tall building

is 4 inches high. An observation

tower in the model is 9 inches

high. How tall is the actual

tower?

Now TryProblem 83

In Example 9, we could have compared the cost of the apples to the number of

apples:

$1.15 isto 5 apples as$cis to16 apples. This would have led to the proportion

If we solve this proportion for c,we obtain the same result: 3.68.

Caution!When solving problems using proportions, make sure that the units

of the numerators are the same and the units of the denominators are the

same. For Example 9, it would be incorrect to write

16 apples

 Cost of 16 apples

1.15 

5



16

 c

Cost of 5 apples 

5 apples

Cost of 16 apples

 16 apples

1.15 

5



c

 16

Cost of 5 apples 

5 apples

436 Chapter 5 Ratio, Proportion, and Measurement

State Sixteen apples will cost $3.68.

CheckIf 5 apples cost $1.15, then 15 apples would cost 3 times as much:

3 $1.15$3.45. It seems reasonable that 16 apples would cost $3.68.

EXAMPLE (^10) Scale Drawings A scaleis a ratio (or rate) that compares
the size of a model, drawing, or map to the size of an actual object. The airplane
shown below is drawn using a scale of 1 inch: 6 feet. This means that 1 inch on the
drawing is actually 6 feet on the plane. The distance from wing tip to wing tip (the
wingspan) on the drawing is 4.5 inches. What is the actual wingspan of the plane?
Analyze

• The airplane is drawn using a scale of 1 inch: 6 feet, which can be written
  as a rate in fraction form as:.


• The wingspan of the airplane on the drawing is 4.5 inches.


• What is the actual wingspan of the plane?
  FormWe will let wrepresent the unknown actual wingspan of the plane. If we
  compare the measurements on the drawing to their actual measurement of the plane,
  we know that those two rates must be equal and we can write a proportion.

1 inch

6 feet

SCALE

1 inch: 6 feet

012 345 6

FT