Final answer:
The charges for Green Grass, Inc. and S & G Lawn Care would be equal after 6.67 hours, not 4 or 5 hours as suggested by the options A and B. To determine when it's better to use either service, two methods could be used: calculating the break-even point or comparing charges at different service hours.
Step-by-step explanation:
To determine when the charges for each company would be equal, you would set the total cost equations for both companies equal to each other and solve for the number of hours of service.
Green Grass, Inc. has an equation of $15 + $10 \times \text{hours}, and S & G Lawn Care has an equation of $35 + $7 \times \text{hours}.
Setting these equal, $15 + $10 \times h = $35 + $7 \times h, where h is the number of hours. Solving for h, we get:
$10h - $7h = $35 - $15
$3h = $20
h = $20 / $3
h = 6.67 hours
So, the charges would be equal after 6.67 hours of service, which is not one of the options provided. Therefore there may be a typo or misunderstanding in the given answers A and B.
There are two methods that could be used to determine the better service:
Method 1: Calculate the break-even point exactly as demonstrated above. This tells you at which point the cost for both services is the same.
Method 2: Compare the total charges at different service hours. This allows you to see which company offers a better deal at specific intervals of time.
Comparing costs at the initial fee is not a valid method as it does not consider the hourly charges which accumulate over time.