Question

Please see image attached. Can you walk me through the steps to solving this type of problem?

Answer 1

For this kind of problem, we have to set the variables, the independent variable, and the dependent variable. In this case, the total cost depends on the number of hours, therefore the independent variable is the number of hours, and the dependent variable is the total cost.

Let x be the number of hours, and y be the total cost in dollars. Since Briana charges $15 plus $2.00 per hour, we can set the following equation:

`y=2x+15.`

Also since Kayla charges $10 plus $3.00 per hour, we can set the following equation:

`y=3x+10.`

Now, once we have the equations, we can graph the equations. In this case, the graphs of both equations are lines.

Recall that to graph a line we only need 2 points on the line, therefore, we substitute x=0 and x=10 in both equations and get:

`\begin{gathered} y=2\cdot0+15=0+15=15, \\ y=2\cdot10+15=20+15=35, \\ y=3\cdot0+10=0+10=10, \\ y=3\cdot10+10=30+10=40. \end{gathered}`

Then, the graph of both equations is:

Finally, the solution to the system of equations is the intersection of the graphs, in this case, the intersection is (5,25).

From the graph, one can determine which service is cheaper depending on the number of hours.