Answer:
[tex]\left\{\begin{array}{l}c\ge 0\\ \\d\ge 0\\ \\c+d\le 11\\ \\9d+6c\ge 60\end{array}\right.[/tex]
2 possible solutions are c = 7, d = 3 and c = 8, d = 2
Step-by-step explanation:
Let d be the number of hours you walk dogs and c be the number of hours you wash cars. Note that [tex]c\ge 0,\ d\ge 0.[/tex]
1. You can work at most 11 hours next week, so
[tex]d+c\le 11[/tex]
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,
[tex]9d+6c\ge 60[/tex]
3. You get following system of inequalities:
[tex]\left\{\begin{array}{l}c\ge 0\\ \\d\ge 0\\ \\c+d\le 11\\ \\9d+6c\ge 60\end{array}\right.[/tex]
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
