A map uses a scale where 3\text{ cm} represents 20\text{ km}. If two towns are separated b… — Armed Services Vocational Aptitude Battery (ASVAB)

A map uses a scale where $3\text{ cm}$ represents $20\text{ km}$ . If two towns are separated by $15\text{ cm}$ on the map, what is the actual distance between them in kilometers?

A
$4$
B
$32$
$100$ Answer
D
$300$

Answer

100

The correct answer is determined by setting up a direct proportion between the map distance and the actual distance:

\frac{3}{20} = \frac{15}{x}

. Cross-multiplying yields

3x = 300

. Dividing both sides by

3

isolates

x

, resulting in

100\text{ km}

. Alternatively, you can observe that the map distance increased by a factor of

5

(

3 \times 5 = 15

), so the actual distance must also increase by a factor of

5

(

20 \times 5 = 100

Step-by-Step Solution

Identify the given scale ratio from the problem.

The ratio of map distance to actual distance is

3\text{ cm} : 20\text{ km}

This baseline ratio establishes the mathematical relationship needed to find any other actual distance.

Set up a proportion matching map measurements to actual measurements.

\frac{3}{20} = \frac{15}{x}

Keeping the units aligned (map distance in the numerator, actual distance in the denominator) ensures the proportion is solvable.

Solve for the unknown actual distance

x

using cross-multiplication.

3x = 15 \times 20 \rightarrow 3x = 300

Cross-multiplication transforms the proportion into a standard linear equation.

Isolate

x

by dividing both sides of the equation by

3

x = \frac{300}{3} = 100

Dividing both sides balances the equation and provides the final actual distance in kilometers.

Key Concept

Direct Proportions and Scale Factors

Question

Answer

Step-by-Step Solution

Key Concept

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