Question

The scale of a map says that 4 cm represents 5 km.

a. What distance on the map (in centimeters) represents an actual distance of 4 kilometers?

cm

b. What is the actual number of kilometers that is represented by 5 centimeters on the map?

km

Answer 1

a. 3.2 cm

b. 6.25 km

Explanation:

Scale problems can be solved with proportions.

a.

4 cm / 5 km = x cm / 4 km

4/5 = x/4

5x = 4 × 4

5x = 16

x = 16/5

x = 3.2

Answer: 3.2 cm

b.

4 cm / 5 km = 5 cm / x km

4/5 = 5/x

4x = 25

x = 25/4

x = 6/25

Answer: 6.25 km

Answer 2

a. 3.2 cm

b. 6.25 km

Explanation:

a.

(4 km)/(5 km) = 0.8

4 km is 0.8 of 5 km, so in the map it is 0.8 of 4 cm.

0.8 * 4 cm = 3.2 cm

Answer: 3.2 cm

b.

(5 cm)/(4 cm) = 1.25

5 cm is 1.25 times 4 cm, so it represents 1.25 * 5 km.

1.25 * 5 km = 6.25 km

Answer: 6.25 km