The system of linear inequalities to model the situation are:
[tex]x+y\leq 20\\\\7.50x+6y\geq 92[/tex]
Solution:
Let "x" be the time spent in dog walking job
Let "y" be the time spent in car wash attendant
Given that,
You can work at most 20 hours next week
"at most" means "less than or equal to" 20
Therefore,
[tex]x+y\leq 20 ---------- eqn 1[/tex]
Also given that,
Your dog- walking job pays $7.50 per hour
Your job as a car wash attendant pays $6 per hour
You need to earn at least $92 to cover you weekly expenses
"at least" means "greater than or equal to" 92
Thus, a inequality is framed as:
[tex]7.50 \times x + 6 \times y \geq 92[/tex]
[tex]7.50x+6y\geq 92 ------------ eqn 2[/tex]
Thus eqn 1 and eqn 2 is the system of linear inequalities to model the situation
