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Assume that​ Tom's Tree and Landscape Service charges ​$ 175 for a consultation fee plus ​$55 per hour for labor and that Lawn Perfect Landscape Service charges ​$325 for a consultation fee plus ​$25 per hour for labor.
​a) Write a system of equations to represent the cost of the two landscaping services.
​b) Graph both equations for 0 to 10 hours on the same axes.
​c) Use the graph to estimate the number of hours of landscaping that must be used for both services to have the same cost.

Respuesta :

Using linear functions, we have that:

a) The system is composed by these following equations: 175 + 55x, 325 + 25x.

b) The graph is given at the end of the answer.

c) From the point of intersection on the graph, both services will have the same cost of $450 for 5 hours of work.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For each function, we have that:

  • The consultation fee is the intercept.
  • The hourly fee is the slope.

Hence the linear equations that compose the system are given by:

175 + 55x, 325 + 25x.

The graph is given at the end of the answer, and from it, the intersection point is at (5,450), meaning that both services will have the same cost of $450 for 5 hours of work.

More can be learned about linear functions at https://brainly.com/question/24808124

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