Question

The Smith family and the Jackson family are having their basements remodeled. The​ Smith's contractor charges​ $16.50 per hour plus​ $289 in supplies. The​ Jackson's contractor charges​ $18.75 per hour and​ $274.60 in supplies. At how many hours of work will the total cost be the same for both​ families?

Answer 1

22hour

Explanation:

$16.50(289)$18.75(274.60)

Answer 2

6.4 hours

Explanation:

Smith's:

`16.5h+289`

16.50 per hour plus supplies.

Jackson's:

`18.75h+274.6`

18.75 per hour pus supplies.

To find the number of hours needed for the cost to be the same, make an equation in which both costs would be equal to each other:

`16.5h+289=18.75h+274.6`

Solve for the value of
`h`. Subtract 289 from both sides:

`16.5h+289-289=18.75h+274.6-289\\16.5h=18.75h-14.4`

Subtract 18.75h from both sides:

`16.5h-18.75h=18.75h-18.75h-14.4\\-2.25h=-14.4`

Divide both sides by -2.25 to isolate h (two negatives makes a positive):

`(-2.25h)/(-2.25)=(-14.4)/(-2.25) \\\\h=6.4`

After 6.4 hours, both costs would be the same, costing $394.60.

Finito.