Charlotte finds two landscape gardeners online: the first charges a fixed fee of $20 per job plus $15 per hour for labor, while the second charges a fixed fee of $90 but only $5 per hour for labor. After how many hours will the second gardener be cheaper than the first?

There are two ways to find the answer to this question.

Way #1:  

Draw both lines on a graph and see where line-1 goes higher than line-2.

In order to do this, you first have to write the equations for both lines, or at least identify the slope and intercept for each one.

Way #2:

If you have to do that anyway, you might as well just find the solutioin of the two equations, and not bother drawing the graph.

First gardener:  Cost1 = 20 + 15H

Second gardener:  Cost2 = 90 + 5H

The second gardener starts out more expensive . . . before they even start working, the first one wants $20 but the second one wants $90.

After that, though, once they start working, their prices come together . . . for every hour they work, the first one wants another $15 but the second one only wants another $5 .

Eventually, after enough hours, their total prices will be equal, and AFTER that, the second one will actually cost less than the first one.

Since we have already written the equations for both of their prices, we can easily (if we have enough scratch paper left over) find the number of hours where their prices are equal.

First gardener:  Cost1 = 20 + 15H

Second gardener:  Cost2 = 90 + 5H

Costs are equal when  20 + 15H = 90 + 5H

Subtract 20 from each side:  15H = 70 + 5H

Subtract 5H from each side:  10H = 70

Divide each side by 10 : H = 7

For less than 7 hours of work, #1 costs less.  For exactly 7 hours of work, they both charge the same amount ($125). For MORE than 7 hours of work, #2 costs less.

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step-by-step explanation:

a.)the line for function b is steeper