Question

You can work at most 20 hours next week. You need to earn at least $92 to cover you weekly expenses.Your dog- walking job pays $7.50 per hour and your job as a car wash attendant pays $6 per hour. Write a system of linear inequalities to model the situation.

Answer 1

The system of linear inequalities to model the situation are:

$x+y\leq 20\\\\7.50x+6y\geq 92$

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,

$x+y\leq 20 ---------- eqn 1$

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:

$7.50 \times x + 6 \times y \geq 92$

$7.50x+6y\geq 92 ------------ eqn 2$

Thus eqn 1 and eqn 2 is the system of linear inequalities to model the situation