Question

You can work at most 11 hours next week. You need to earn at least $60 to cover your weekly expenses. Your dog-walking job pays $9 per hour and your job as a car wash attendant pays $6 per hour. Let d = the # of hours you walk dogs and c = the # of hours you wash cars.

Write a system of linear inequalities representing the situation and identify 2 solutions to the system.

Answer 1

Answer: d + c < 11

9d + 6c > 60

2 solutions (d, c):

(5, 6)

(6, 5)

Explanation:

Answer 2

`\left\{\begin{array}{l}c\ge 0\\ \\d\ge 0\\ \\c+d\le 11\\ \\9d+6c\ge 60\end{array}\right.`

2 possible solutions are c = 7, d = 3 and c = 8, d = 2

Explanation:

Let d be the number of hours you walk dogs and c be the number of hours you wash cars. Note that
`c\ge 0,\ d\ge 0.`

1. You can work at most 11 hours next week, so

`d+c\le 11`

2. Your dog-walking job pays $9 per hour, so for d hours you will earn $9d. Your job as a car wash attendant pays $6 per hour, then for c hours you will be paid $6c. In total, you will earn $(9d+6c) that must be at least $60.

So,

`9d+6c\ge 60`

3. You get following system of inequalities:

`\left\{\begin{array}{l}c\ge 0\\ \\d\ge 0\\ \\c+d\le 11\\ \\9d+6c\ge 60\end{array}\right.`

The diagram shows the solution set to the system of these inequalities.

2 possible solutions are c = 7, d = 3 and c = 8, d = 2