Question

A high school is expanding its football field in order to allow other sports to be played on the field. The school will also be installing artificial turf, which costs $4.75 per square foot, on the entire field. The current football field is 360 feet long and 160 feet wide. The number of feet, x, by which the length of the field will be expanded is twice the number of feet by which the width of the field will be expanded. Which function f(x) represents the cost of artificial turf for the entire field?

A) $4.75(360 + 2x)(160 + x)
B) $4.75(360 + x)(160 + 2x)
C) $4.75(360 + x)(160 + x)
D) $4.75(360 + 2x)(160 + 2x)

Answer 1

The function that represents the cost of artificial turf for the entire field is $4.75(360 + 2x)(160 + x). The function f(x) represents the cost of artificial turf for the entire expanded football field. To find the correct function, we need to consider the current dimensions of the field and how much it is expanding by.

Step-by-step explanation:

The function that represents the cost of artificial turf for the entire field is $4.75(360 + 2x)(160 + x). Let's break down the problem step by step:

1. According to the question, the length of the field will be expanded by twice the amount of the width, so the length will be increased by 2x and the width will be increased by x.
2. The area of the field is calculated by multiplying the length by the width, which gives us (360 + 2x)(160 + x).
3. Finally, to find the cost, we multiply the area by the cost per square foot, which is $4.75. Therefore, the function that represents the cost is $4.75(360 + 2x)(160 + x).

Given the current length is 360 feet, width is 160 feet, and the length x will be twice the width it expands by, the correct function is f(x) = $4.75(360 + 2x)(160 + x). This represents the cost per square foot multiplied by the area of the expanded field.