Question

Jeremy is looking at two different lawncare companies to weed and mulch his garden.

Greenscape Lawncare charges $100 for the mulch, plus $12 per hour for the labor.
DJ's Lawncare charges $23 per hour, which includes the price for the mulch. What is
maximum number of hours for which DJ's Lawncare is the better deal?
a. Define a variable.
b. Write and solve an equation.
c. Answer in a sentence.

Answer 1

DJ's will be the better deal for jobs of 9.091 hours or less.

Explanation:

Let x be the number of hours of lawncare.

Greenscape Lawncare Cost (G)

G = $12x + $100

DJ's Lawncare (D)

D = $23x

Better Deal

We can see that DJ's will be the better deal for lawns requiring a shorter number of hours, since the mulch is already included in the price. A 1 hour job would cost $112 with Greenscape but only $23 with DJ's.

But the question is at what number of hours does Greenscape become the better deal?

Let's find the number of hours at which both companies would charge the same amount:

G = $12x + $100

D = $23x

Set G = D

$12x + $100 = $23x

$11x = $100

x = (100/11) hours or 9.091 hours.

DJ's will be the better deal for jobs of 9.091 hours or less.

Sentence:

DJ's Lawncare will be the better deal for jobs up to 9.091 hours, despite the higher per hour charge of $23. because the mulch is already included in the price.