Question

jeremy is looking for two different lawncare companies to weed and mulch his flower beds. greenscape charges $100 for the mulch plus $12 per hr for labor. D&J landscape charges $23 per hr for the job including the mulch. what is the minimum number of hours the job could be for D&J Landscape to have the better deal?

Answer 1

The D&J Landscape will have to spend less than 9.09 hours in order to be more cost effective.

Explanation:

Greenscape charges $100 for the mulch plus $12 per hr for labor.

D&J landscape charges $23 per hr for the job including the mulch.

Let x be the total number of hours.

Amount charge by Greenscape =
`y_(1) = 12x+100`

Amount charged by D&J landscape =
`y_(2) =23x`

Equating both the equations.

`12x+100 = 23x`

Solving for x;

`11x = 100`

`x= (100)/(11)`

x = 9.09 hours.

Hence, for the D&J landscape company, the minimum hours should be x<9 so as to have a better deal.

Answer 2

Let x represent the number of hours and y represent the total cost

Greenscape equation: y = 12x + 100

D&J Landscape equation: y = 23x

Use substitution to find out how many hours for the cost to be the same.

23x = 12x + 100

11x = 100

x =
`(100)/(11)` ≈ 9.1 hours

D&J Landscape is a better deal when the job takes less than 9.1 hours.