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.

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

To write a system of inequalities, let's assign variables to represent the number of hours worked at each job. Let's use "h" to represent the number of hours worked in house cleaning and "s" to represent the number of hours worked in the sales job.

We know that the total number of hours worked should not exceed 34, so we can write the first inequality:
h + s ≤ 34

Next, we need to consider the minimum amount of money needed to cover expenses, which is at least $245 per week. To calculate the total income, we multiply the number of hours worked by the respective wage for each job.

For house cleaning, the income can be calculated as $8 per hour worked:
Income from house cleaning = 8h

For the sales job, the income can be calculated as $6 per hour worked:
Income from sales job = 6s

The total income from both jobs should be at least $245, so we can write the second inequality:
8h + 6s ≥ 245

Therefore, the system of inequalities representing the various numbers of hours you can work at each job is:
h + s ≤ 34
8h + 6s ≥ 245