Question

practice: proportions
score: 5/6 answered: 5/6
question 6
the scale on a map indicates that 1 centimeter on the map corresponds to an actual distance of 30 kilometers. if two cities are approximately 3.6 centimeters apart on the map, then what is the actual distance between them?
translate to a proportion:
two cities are approximately 3.6 centimeters apart on the map, then the actual distance is
kilometers.
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Explanation:

Step1: Define variables and proportion

Let \( x \) be the actual distance in kilometers. The scale gives a ratio of map distance to actual distance: \( \frac{1\ \text{cm}}{30\ \text{km}}=\frac{3.6\ \text{cm}}{x\ \text{km}} \).

Step2: Solve the proportion

Cross - multiply: \( 1\times x = 30\times3.6 \).
Calculate \( 30\times3.6 = 108 \). So \( x = 108 \).

Answer:

Translate to a proportion: \(\boldsymbol{\frac{1}{30}=\frac{3.6}{x}}\) (where \( x \) is the actual distance in kilometers)
The actual distance is \(\boldsymbol{108}\) kilometers.