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.
1.If h represents the number of labor hours and C represents the cost, write the total cost equation for Greener Lawns.
2.If h represents the number of labor hours and C represents the cost, write the total cost equation for Lawns for Less.
3.Solve the system of equations for the total cost of lawn care using the desired technique: substitution, elimination, or graphing.
4.Document how you came to these conclusions for accuracy.
1. The total cost equation for Greener Lawns can be written as C = 200 + 50h.
Explanation: The initial fee of $200 is a fixed cost that is added regardless of the number of labor hours. The labor costs are then added at a rate of $50 per hour of labor (h), resulting in a linear relationship between the total cost (C) and the number of labor hours.
2. The total cost equation for Lawns for Less can be written as C = 300 + 25h.
Explanation: Similarly, the initial fee of $300 is a fixed cost, and the labor costs are added at a rate of $25 per hour of labor (h).
3. To solve the system of equations to find the total cost of lawn care, we can use the substitution method.
Start with the equations:
C = 200 + 50h (Equation 1)
C = 300 + 25h (Equation 2)
From Equation 1, we can express C in terms of h:
C = 200 + 50h (Equation 1)
Substitute this expression for C in Equation 2:
200 + 50h = 300 + 25h
Simplify and rearrange the equation:
50h - 25h = 300 - 200
25h = 100
h = 100/25
h = 4
Substitute the value of h back into Equation 1 or Equation 2 to find the total cost:
C = 200 + 50(4)
C = 200 + 200
C = 400
Therefore, the total cost of lawn care for Greener Lawns when 4 hours of labor are used is $400.
4. To determine the total cost equations for Greener Lawns and Lawns for Less, we analyzed the given information about their pricing structures and expressed them in terms of the number of labor hours (h) and the total cost (C). We used the substitution method to solve the system of equations, substituting one equation into another to eliminate one variable and find the value of h. Finally, we substituted the value of h back into one of the equations to find the total cost (C).