Question

Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: 15x+10y>110 . Is (60, 20) a solution? How do you know? What does this point represent?

Answer 1

The first step is to ignore the inequality symbol first and replace it with '=' sign. Then, find the x- and y-intercepts.

15x + 10y = 1,100

x-intercept:

15x + 0 = 1,100

x = 1,100/15 = 73.33

y-intercept:

0 + 10y = 1,100

y = 1,100/10 = 110

Now, plot points (73.33,0) and (0,110). Since the equality symbol is ≥, which has an equal sign to it, connect the points using a solid line.

Next, let's find a point on the graph. Suppose it is the origin at (0,0). Use this points to the equation.

15x + 10y ≥ 1,100

15(0) + 10(0) ? 1,100

0 ? 1,100

0 < 1,100

It makes the symbol ≥ false. Therefore, it means that the other region bounded by the line is the solution. So, you shade this area. The final graph is shown in the picture attached.

Answer 2

Yes. When you plug in the points (60,20) the equation is correct. 15(60)+10(20) ? 1100 = 900+200 ? 1100 = 1100 ? 1100. The points represent number of hours Ezra mowed lawns and walked dogs.

Explanation:

The coordinate pair (60, 20) is a solution because it satisfies the inequality 15x + 10y greater than or equal to 1100

The coordinate pair (60, 20) is a solution because Ezra earns 60 x $15 = $900 mowing lawns and 20 x $10 = $200 walking dogs, for a total of $1100.

Ezra can spend 60 hours mowing lawns and 20 hours walking dogs to earn enough money for the laptop.