Dillon is enrolled in an SAT prep class at the Princeton Community Center. The community center is 4 kilometers away from Dillon's house. On a map of Princeton, this distance is represented by 8 centimeters. What is the scale of the map?

Question

Write your answer in simplest form using whole numbers.

centimeters :
kilometers

Answer 1

To determine the scale of the map, we first need to express the distance on the map (8 centimeters) and the actual distance (4 kilometers) in the same units.

1. We already have the map distance which is 8 centimeters.
2. The actual distance is 4 kilometers. To convert kilometers to centimeters, we use the conversion factor: \[ 1 \text{ kilometer} = 1000 \text{ meters} \] \[ 1 \text{ meter} = 100 \text{ centimeters} \] Therefore, \[ 1 \text{ kilometer} = 1000 \times 100 = 100000 \text{ centimeters} \] So, for 4 kilometers: \[ 4 \text{ kilometers} = 4 \times 100000 = 400000 \text{ centimeters} \]

Now we have:

• Map distance = 8 centimeters
• Actual distance = 400000 centimeters

Next, we can express the scale as: \[ \text{Scale} = \text{map distance} : \text{actual distance} = 8 \text{ cm} : 400000 \text{ cm} \]

To simplify this ratio, we can divide both sides by 8: \[ \frac{8}{8} : \frac{400000}{8} = 1 : 50000 \]

So, the scale of the map in simplest form is: \[ \boxed{1 : 50000} \]