Question

Chance has hired a construction crew to renovate his kitchen. They charge $3.14 per square foot for materials and $128.37 per day of labor. Chance spent $3,362.19 on the renovation. If the number of square feet is 275 more than the number of days it took for the renovation, how long did the renovation take?

Answer 1

The renovation took approximately 19 days.

Step-by-step explanation:

To find out how long the renovation took, we need to set up an equation based on the given information. Let x be the number of days it took for the renovation. According to the problem, the number of square feet is 275 more than the number of days, so the number of square feet is x + 275.

The total cost of the renovation is given as $3,362.19. This can be expressed as the cost of materials plus the cost of labor: 3.14(x + 275) + 128.37(x) = 3362.19. Solving this equation will give us the value of x, which represents the number of days it took for the renovation.

Step 1: Simplify the equation: 3.14x + 868.5 + 128.37x = 3362.19.

Step 2: Combine like terms: 3.14x + 128.37x + 868.5 = 3362.19.

Step 3: Combine coefficients: 131.51x + 868.5 = 3362.19.

Step 4: Subtract 868.5 from both sides: 131.51x = 2493.69.

Step 5: Divide both sides by 131.51: x ≈ 18.95.

Therefore, the renovation took approximately 19 days.