Question

Chance has hired a construction crew to renovate his kitchen. They charge $3.55 per square foot for materials and $121.26 per day of labor. Chance spent $2,450.24 on the renovation. If the number of square feet is 198 more than the number of days it took for the renovation, how long did the renovation take? A. 14 days B. 12 days C. 3 days D. 17 days

Answer 1

The renovation took 14 days ⇒ answer A

Step-by-step explanation:

Chance has hired a construction crew to renovate his kitchen

• They charge $3.55 per square foot for materials
• They charge $121.26 per day of labor
• Chance spent $2,450.24 on the renovation
• The number of square feet is 198 more than the number of days it took for the renovation

We need to find for how long the renovation took

Assume that the renovation took x days

∵ The renovation took x days

∵ The number of square feet is 198 more than the number of days

∴ The number of square feet = x + 198

∵ They charge $3.55 per square foot

∵ They charge $121.26 per day of labor

∴ The cost of renovation = 3.55(x + 198) + 121.26(x)

- Simplify the expression

∴ The cost of renovation = 3.55 x + 702.9 + 121.26 x

- Add like terms

∴ The cost of renovation = 124.81 x + 702.9

∵ Chance spent $2,450.24 on the renovation

- Equate the cost of renovation by the money that Chance spent

 on the renovation

∴ 124.81 x + 702.9 = 2,450.24

- Subtract 702.9 from both sides

∴ 124.81 x = 1,747.34

- Divide both sides by 124.81

∴ x = 14

The renovation took 14 days

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