A map has a scale where 2 centimeters represents 15 kilometers. If the distance between tw… — SAT

A map has a scale where $2$ centimeters represents $15$ kilometers. If the distance between two cities on the map is $8$ centimeters, what is the actual distance between the two cities, in kilometers?

Answer: 60 kilometers

Answer

The actual distance between the two cities is

60

kilometers.

The correct answer is

60

. The map scale is

2

centimeters to

15

kilometers. The map distance between the cities is

8

centimeters, which is

4

times the scale distance of

2

centimeters (since

8 \div 2 = 4

). Therefore, the actual distance between the cities is

4

times the scale distance of

15

kilometers, which is

15 \times 4 = 60

kilometers.

Step-by-Step Solution

Set up a proportion using the map scale ratio of centimeters to kilometers.

\frac{2}{15} = \frac{8}{x}

This establishes that the ratio of map distance to actual distance remains constant.

Solve for the unknown actual distance,

x

, by cross-multiplying.

2x = 120

Multiplying the numerator of each fraction by the denominator of the other solves the proportion.

Divide by the coefficient of

x

to find the final actual distance.

x = 60

Dividing

120

2

isolates

x

and gives the actual distance in kilometers.

Key Concept

Setting up and solving proportions using scale factors.

Question

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Step-by-Step Solution

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