Question

Given the cost equations for two landscaping services (Tom's Tree and Lawn Perfect), what number of labor hours would make their costs equal if Tom's Tree charges $250 for consultation and $45 per hour, and Lawn Perfect charges $400 for consultation and $20 per hour?

a) 15 hours
b) 20 hours
c) 25 hours
d) 30 hours

Answer 1

The number of labor hours that would make the costs of Tom's Tree and Lawn Perfect equal is 6 hours.

Step-by-step explanation:

To find the number of labor hours that would make the costs of Tom's Tree and Lawn Perfect equal, we need to set up the cost equations for both services and solve for the number of hours.

Let x represent the number of labor hours.

The cost equation for Tom's Tree is $250 + $45(x).

The cost equation for Lawn Perfect is $400 + $20(x).

To find the number of labor hours when the costs are equal, we set the two equations equal to each other:

$250 + $45(x) = $400 + $20(x)

Simplifying the equation, we get:

$45(x) - $20(x) = $400 - $250

Combining like terms, we have:

$25(x) = $150

Dividing both sides by $25, we find:

x = 6

Therefore, it would take 6 labor hours for the costs of Tom's Tree and Lawn Perfect to be equal.