Proportional Reasoning Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
A map uses a scale of 1 cm : 25 km. Two cities are 7.5 cm apart on the map. What is the actual distance?

Solution

  1. 1
    Set up the proportion: 1 cm25 km=7.5 cmx km\frac{1 \text{ cm}}{25 \text{ km}} = \frac{7.5 \text{ cm}}{x \text{ km}}.
  2. 2
    Solve: x=25×7.5=187.5x = 25 \times 7.5 = 187.5 km.

Answer

187.5 km187.5 \text{ km}
Scale problems are a direct application of proportional reasoning. Multiply the map measurement by the scale factor to find the real-world distance.

About Proportional Reasoning

The ability to recognize and work with multiplicative relationships between quantities. If one quantity doubles, a proportional quantity also doubles — the ratio stays constant.

Learn more about Proportional Reasoning →

More Proportional Reasoning Examples

Example 1 easy

If 3 notebooks cost $7.50, how much do 7 notebooks cost?

Example 2 medium

A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 9 cups of sugar, how many c

Example 4 easy

A recipe that serves 4 people uses 10 cups of flour. How many cups are needed to serve 10 people?

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