Gabriella is deciding between two landscaping companies for her place of business.Company A charges $45 per hour and a $275 equipment fee. Company B charges $65per hour and a $175 equipment fee. Let A represent the amount Company A wouldcharge for t hours of landscaping, and let B represent the amount Company B wouldcharge for t hours of landscaping. Write an equation for each situation, in terms of t,and determine which company would be cheaper if Gabriella needs 3 hours oflandscaping

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JuliannU383494 JuliannU383494 · Answer 1 · 2022-10-25T19:47:10+02:00

We can model both situations with the equation of a straight line. Remember that such expression is:

[tex]y=mx+b[/tex]

Where m is the slope, and b is the intercept with the x axis.

For this kind of situations, b would mean a fixed fee (equipment fee, in this case) and m would mean a variable fee (fee per hour of work)

In the context of the problem, that would mean that:

[tex]\begin{gathered} A=45t+275 \\ B=65t+175 \end{gathered}[/tex]

Where t is the hours of work elapsed.

If we want to find out how much does each company charge for the 3 hours of

landscaping Gabriella needs, we'll just ned to replace t for 3

[tex]\begin{gathered} A=45(3)+275\text{ }\rightarrow\text{ }A=410 \\ B=65(3)+175\text{ }\rightarrow\text{ }B=370 \end{gathered}[/tex]

So company B would be cheaper.