algebra 1 (ASAP)

Question

1. Green Grass, Inc. charges an initial fee of $15 plus $10 per hour for lawn services. Their main competitor, S & G Lawn Care, charges an initial fee of $35 plus $7 per hour.
2. When would the charges for each company be equal?
3. When would it be better to use Green Grass, Inc. and when would it be better to use their competitor, S & G Lawn Care?

Answer 1

a) Let P be how much a company charges, and h be the number of hours.

For Green Grass Inc. their price can be written as P_GG = 15 + 10h and

S and G Lawn Care's price can be written as P_SG = 35 + 7h.

To figure out when the prices are equal, set P_GG = P_SG

Therefore, 15 + 10h = 35 + 7h. Solving gives h = 20/3 hours or 6hours 40min.

b) Green Grass Inc starts out charging less since their initial fee is $15 while their competitor's is 35$. However, Green Grass Inc would eventually overcome S and G Lawn Care's charge because Green Grass charges more per hour. For the first 6 hours and 40 minutes Green Grass Inc charges less so it would be better to use them. Then at 6 hours and 40 minutes, they charge the same. Then Green Grass Inc overcomes S and G Lawn Care, and any time greater than 6 hours and 40 minutes, S and G Lawn Care charges less.

Answer 2

The cost depends on how many hours are used.

The cost of using Green Grass:

GG(hours) = $15 + $10*hours

The cost of using S&G:

SG(hours) = $35 + $7*hours

a. The 2 are equal for the number of hours that results in

GG(hours) = SG(hours)

$15 + $10*hours = $35 + $7*hours

solving for hours:

$3*hours = $20

hours = 20/3 = 6 hours and 40 minutes

b. It's better to use GG for jobs less than 20/3 hours.

It's better tp SG for jobs greater than 20/3 hours.