Question

You can work a total of no more than 34 hours per week at your two jobs. House cleaning pays $8 per hour and your sales job pays $6 per hour. You need to earn at least $245 per week to cover your expenses. Write a system of inequalities that shows the various numbers of hours you can work at each job.

Answer 1

Your total pay for the 2 jobs must be at least 245 dollars.

Pay1 + Pay2 >= 245


The pay for your first job, cleaning, is 8 dollars times the number of hours, h, worked at that job.

Pay1 = 8h

So:

8h + Pay2 >= 245


The pay for your second job, sales, is 6 dollars times the number of hours worked at that job.

Pay2 = 6 * SalesHours
or
Pay2 = 6x

So:

8h + 6x >= 245

That's one inequality.



We also know that the total number of hours worked, h + x, cannot exceed 34. So:

h + x <= 34

There's a second inequality. Almost done.



It is impossible to work less than 0 hours at a job, so both h and x, individually, can be a minimum of 0. Therefore:

h >= 0 <= x



So the final set of inequalities is as follows:

8h + 6x >= 245
h + x <= 34
h >= 0 <= x