Break-Even Analysis and Cost Analysis: As a first-time homeowner, there are going to many decisions that you need to make, such as whom to hire for the upkeep of your lawn. You have just received advertisements from 2 companies in your area: Greener Lawns and Lawns for Less. Greener Lawns charges an initial fee of $200, plus $50 per hour for labor costs. Lawns for Less charges an initial fee of $300, plus $25 per hour for labor costs.
If h represents the number of labor hours and C represents the cost, write the total cost equation for Greener Lawns.
If h represents the number of labor hours and C represents the cost, write the total cost equation for Lawns for Less.
Solve the system of equations for the total cost of lawn care using the desired technique: substitution, elimination, or graphing.
Document how you came to these conclusions for accuracy
To determine the total cost equations for Greener Lawns and Lawns for Less, we need to consider the initial fees and the labor costs.
Total cost equation for Greener Lawns:
The initial fee for Greener Lawns is $200, which is a constant cost. The labor costs are $50 per hour, so we can represent that as $50h (where h is the number of labor hours). Therefore, the total cost equation for Greener Lawns can be written as:
C(g) = 200 + 50h
Total cost equation for Lawns for Less:
The initial fee for Lawns for Less is $300, which is again a constant cost. The labor costs are $25 per hour, represented as $25h (where h is the number of labor hours). Hence, the total cost equation for Lawns for Less is:
C(l) = 300 + 25h
Now, to solve the system of equations for the total cost of lawn care, we can use the desired technique: substitution, elimination, or graphing.
Substitution:
In substitution, we solve one equation for one variable and substitute that value into the other equation. We can solve C(g) = C(l) for h using substitution.
C(g) = C(l)
200 + 50h = 300 + 25h
Simplify the equation by subtracting 25h from both sides:
200 + 25h = 300
Subtract 200 from both sides:
25h = 100
Divide both sides by 25:
h = 4
The number of labor hours, h, is 4. Now we can substitute this value back into either equation to find the total cost.
Let's substitute h = 4 into the total cost equation for Greener Lawns:
C(g) = 200 + 50h
C(g) = 200 + 50(4)
C(g) = 200 + 200
C(g) = 400
The total cost for Greener Lawns is $400.
Similarly, substituting h = 4 into the total cost equation for Lawns for Less:
C(l) = 300 + 25h
C(l) = 300 + 25(4)
C(l) = 300 + 100
C(l) = 400
The total cost for Lawns for Less is $400.
Therefore, both companies have the same total cost of $400 for 4 labor hours.
Note: This explanation assumed that the total cost is determined only by the initial fee and labor costs and did not consider any other potential factors that might affect the total cost of lawn care from these companies.