Question

You can work a maximum of 40 hours a week . You need to make 400$ in order to cover your expenses. Your office job pays 12$ and hour and your babysitting job pays 10$ an hour. Write a system of inequalities to model this situation.

Answer 1

To cover expenses of $400 with a maximum of 40 hours of work per week, the system of inequalities will consist of: 12x + 10y ≥ 400 for weekly earnings and x + y ≤ 40 for total hours worked, along with x ≥ 0 and y ≥ 0 to represent non-negative work hours.

Step-by-step explanation:

The student needs to make $400 a week and can work a maximum of 40 hours across two jobs. If we let x be the number of hours worked at the office job and y be the hours spent babysitting, the system of inequalities to model this situation can be set up as follows:

• 12x + 10y ≥ 400: This inequality represents the total earnings from both jobs being at least $400.
• x + y ≤ 40: This inequality makes sure the total hours worked do not exceed 40 hours.
• x ≥ 0 and y ≥ 0: These inequalities represent that the number of hours worked at each job cannot be negative.

These inequalities ensure that the student is able to cover their expenses by working at most 40 hours a week and earning at least $400 from the two jobs combined. With $12 and $10 as the respective hourly wages, the student has the flexibility to adjust the hours between the two jobs as long as they satisfy both constraints.

Answer 2

have o as the hours you work in the office, and b as the hours for babysitting
you can work at most 40 hours: o+b<=40
you need >=400$ and get paid 12$(o) and 10$(b)
12*o+10*b>=400