Gonzalez Howell
10/22/2023 · Middle School
A scale on a map 3 cm represents 5 km . What distance on the map (in centimeters) represents an actual distance of 3 km ?
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Step-by-step Solution
To find the distance on the map that represents an actual distance of 3 km, we can use the scale provided.
Given:
- 3 cm on the map represents 5 km in real life.
We need to find:
- The distance on the map that represents 3 km in real life.
Let's denote the distance on the map as \( x \) cm.
Using the scale, we can set up a proportion to find the distance on the map that represents 3 km:
\[
\frac{3 \text{ cm}}{5 \text{ km}} = \frac{x \text{ cm}}{3 \text{ km}}
\]
Now, we can solve for \( x \) to find the distance on the map that represents 3 km.
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{3}{5}=\frac{x}{3}\)
- step1: Swap the sides:
\(\frac{x}{3}=\frac{3}{5}\)
- step2: Multiply both sides of the equation by \(3:\)
\(\frac{x}{3}\times 3=\frac{3}{5}\times 3\)
- step3: Multiply the terms:
\(x=\frac{3\times 3}{5}\)
- step4: Evaluate:
\(x=\frac{9}{5}\)
The distance on the map that represents an actual distance of 3 km is \(1.8\) cm.
Quick Answer
The distance on the map that represents 3 km is 1.8 cm.
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