Question

In order to save money for prom, Tom is going to walk his neighbor's dog for $6an hour and wash cars for $7.50 an hour. His mother told him he is not allowedto work more than 15 hours in order to keep up with his homework. If Tomwould like to make at least $75 to cover prom expenses, help him determinecombination of hours he can work between the 2 jobs.A. Write and graph a system of linear inequalities.B. What are 2 possible solutions?

Answer 1

Let's use the variable x to represent the number of hours walking the dog and the variable y to represent the number of hours washing cars.

If he can work a maximum of 15 hours, we have the inequality:

`x+y\le15`

Also, if he wants to make at least $75, we have the inequality:

`6x+7.5y\ge75`

In order to graph these inequalities, let's find two points that are on the line of the corresponding equation:

`\begin{gathered} x+y=15 \\ (7,8)\text{ and }(8,7) \\ 6x+7.5y=75 \\ (0,10)\text{ and }(5,6) \end{gathered}`

Now, graphing each inequation with the corresponding solution area (first one in blue, second one in green, common region in orange), we have:

Analysing the options, two of them that are inside the solution area are 4 hrs dog walking and 8 hrs car washing (A) and 10 hrs dog walking and 3 hrs car washing (C).