Question

Andrea works at two different jobs. She works no more

than 40 hours per week combined between the two jobs.
At one job, she makes $12 per hour. At her other job, she
makes $16 per hour. Each week she earns at least $460.
Andrea writes a system of inequalities to represent this
situation. One of her inequalities is shown below.
x+y≤40
What should be the other inequality in Andrea's system
of inequalities?

Answer 1

Second inequality is
12x + 16y ≥ 460

We also have implied inequalities x ≥ 0, y ≥ 0 meaning hours cannot be negative

Explanation:

The other equality refers to the earnings

Let x be the hours worked in the first job
Earnings at $12 per hour = 12x

Let y be the hours worked in the second job
Earnings at $16 per hour = 16y

Total earnings = 12x + 16y
This must be at least $460
"at least" means ≥

So second inequality is
12x + 16y ≥ 460