This is a scale drawing of an actual park. What percent of the park is the playground?

Question

Start by finding the area of the entire park on the map.
A scale map of a park with dimensions 20 in by 20 in. Within the park are a picnic area and a playground with dimensions 16 in by 5 in.
The area of the entire park is
400
square in.
Excellent!
Next, find the area of the playground on the map.
A scale map of a park with dimensions 20 in by 20 in. Within the park are a picnic area and a playground with dimensions 16 in by 5 in.
The area of the playground is
80
square in.
Good work!
To find the percent of the park that is the playground, start by setting up the double number line. Show that the area of the entire park is 400 square in on the map.
Area (square in)
0

400
0%

100
%
Great job!
Next, partition the double number line so that you can show the area of the playground, 80 square in.
Area (square in)
0
400
0%
100%

Answer 1

To find the percent of the park that is the playground, we can set it up step by step:

1. Find the total area of the park:
   The area of the park is 400 square inches.

2. Find the area of the playground:
   The area of the playground is 80 square inches.

3. Calculate the percentage of the park that is the playground:
   The formula for calculating the percentage is:

   \[ \text{Percentage} = \left( \frac{\text{Area of the playground}}{\text{Area of the park}} \right) \times 100 \]

   Substitute the values:

   \[ \text{Percentage} = \left( \frac{80 \text{ sq in}}{400 \text{ sq in}} \right) \times 100 = 20% \]

Therefore, the playground makes up 20% of the park.

Double Number Line

To represent this on a double number line:

• On the top line (area in square inches):
  0 80 400
  (Playground) (Park)

• On the bottom line (percentage):
  0% 20% 100%
  (Playground) (Park)

The playground area corresponds to 20% of the total park area.