At an elementary school there are two fenced in areas on the playground. The small play area is 14
1
4
the area of the large play area. The total square footage of the two areas is 2000 ft2
ft
2
. What is the size of the small play area?
Responses
A 200 ft2
ft
2
200 ft 2
B 1600 ft2
ft
2
1600 ft 2
C 800 ft2
ft
2
800 ft 2
D 400 ft2
The correct answer is C.
Let's use x to represent the size of the small play area.
We know that the large play area is 14 1/4 times the size of the small play area:
L = 14 1/4 x
And we know that the total area of both play areas is 2000 ft2:
x + 14 1/4 x = 2000
Simplifying this equation:
15 1/4 x = 2000
x = 800
Therefore, the small play area is 800 ft2.
To determine the size of the small play area, we can start by setting up an equation based on the given information.
Let's assume the area of the small play area is x ft2.
According to the given information, the large play area is 14 1/4 times the area of the small play area, which can be written as:
Area of large play area = 14 1/4 * x ft2
The total square footage of the two areas is given as 2000 ft2, so we can set up the equation:
x + (14 1/4 * x) = 2000
Now, we can simplify the equation:
15 1/4 * x = 2000
To solve for x, we divide both sides of the equation by 15 1/4:
x = 2000 / 15 1/4
To simplify further, let's convert the mixed number into an improper fraction:
x = 2000 / (61/4)
To divide by a fraction, we can multiply by its reciprocal:
x = 2000 * (4/61)
Evaluating this expression:
x ≈ 130.82 ft2
So, the size of the small play area is approximately 130.82 ft2.
Therefore, the correct answer is not listed among the options provided.