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.

Question

09-09-2022
Mathematics

contestada

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.

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joaobezerra joaobezerra · Answer 1 · 2022-09-09T23:36:25+02:00

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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