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Difficulty: EasyRatios, Rates, and Proportions

On a map of a city, the scale is 0.5 inches=12 miles0.5\text{ inches} = 12\text{ miles}. If the actual distance between two towns is 96 miles96\text{ miles}, what is the distance between the two towns on the map, in inches?

  1. A
    2
  2. 4Answer
  3. C
    8
  4. D
    16
  5. E
    48

Answer

4 inches
To find the distance on the map, we set up the proportion comparing map inches to actual miles: 0.5 inches12 miles=x inches96 miles\frac{0.5\text{ inches}}{12\text{ miles}} = \frac{x\text{ inches}}{96\text{ miles}}. Cross-multiplying gives 12x=4812x = 48, which simplifies to x=4x = 4. Therefore, the distance on the map is 4 inches4\text{ inches}.

Step-by-Step Solution

1
Set up a proportion to relate the map distance to the actual distance.
0.5 inches12 miles=x inches96 miles\frac{0.5\text{ inches}}{12\text{ miles}} = \frac{x\text{ inches}}{96\text{ miles}} where xx represents the distance between the two towns on the map.
This establishes a direct proportion based on the map's scale.
2
Solve for the unknown variable xx by cross-multiplying.
12⋅x=0.5⋅9612 \cdot x = 0.5 \cdot 96
12x=4812x = 48
Cross-multiplication is the standard algebraic method to solve proportions.
3
Divide both sides of the equation by 12 to find xx.
x=4812=4x = \frac{48}{12} = 4
Isolating the variable gives the final map distance.

Key Concept

Solving ratio scale problems by setting up and solving proportions.
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Topics

Ratios, Rates, and Proportions

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