Question

The city wants to build a football field. Each wheelbarrow full of dirt covers an area of 10x squared. Determine how many wheelbarrows full of dirt they need for the field below.

One side of the rectangle is just 5x squared. The other side is 10x square plus 90x.

Answer 1

As this is a unitless problem, let us try to deal with it as if it does have units. Since we are already given the length and width of a rectangle, we can solve for the area by multiplying. After getting the area, we divide this by the area a wheelbarrow can cover to obtain the expression for how many wheelbarrows we need.

Rectangle length = 10x^2 + 90x
Rectangle width = 5x^2
Rectangle area = length * width = 5x^2(10x^2 + 90x)

Rectangle area = 50x^4 + 450x^2

Dividing:

_5x^2_+_45____10x^2|50x^4 + 450x^2 50x^4 -------- 450x^2 450x^2 --------- 0

Therefore, the expression for how many wheelbarrows are to be used is 5x^2 + 45 wheelbarrows.