Question

Luis is building a new deck and needs to have a slab of concrete poured. He knows the contractor charges an initial cost of $75 plus an additional $2.50 per square foot of concrete. Which equation can be used to determine the cost (y), in dollars, to pour the concrete slab with an area of x square feet?

A) y = 2.5x + 75
B) y = 75x + 2.5
C) y = 75 + 2.5x
D) y = 2.5 + 75x

Answer 1

The correct equation to determine the cost to pour a concrete slab based on its area in square feet is y = 2.5x + 75, where y represents the total cost and x represents the square footage.

Step-by-step explanation:

Luis is looking to determine the cost (y), in dollars, to pour a concrete slab with an area of x square feet. The contractor charges an initial cost of $75 plus an additional $2.50 per square foot of concrete. To represent this situation mathematically, we use a linear equation, which expresses the total cost as a combination of the initial cost and the cost per unit area.

The correct equation is:

y = 2.5x + 75

This equation is derived from the understanding that the total cost (y) can be split into two components:

• The initial cost, which is a fixed amount regardless of the size of the slab ($75), and
• The variable cost, which depends on the area of the concrete slab being poured ($2.50 per square foot).

Therefore, for x square feet of concrete, the variable cost would be 2.5x dollars. Adding this to the initial cost provides the total cost y.