Question

Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week.

-Write up a system of linear inequalities to represent the situation.

I really need help, I don't really understand this even after looking back at notes.

Answer 1

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Answer:

• m + b ≤ 15
• 3m + 5b ≥ 60

Explanation:

There are two requirements:

1. the need to limit time
2. the need for a certain income

Each of these gives rise to an inequality.

The variables in the problem are the numbers of hours spent at each activity. If we let m represent hours mowing, and b represent hours babysitting, then we have ...

m + b ≤ 15 . . . . . . . . total hours can be no more than 15

The amount of money earned mowing is 3m. The amount of money earned babysitting is 5b. We want the total earned to be at least $60, so the other constraint can be expressed as ...

3m +5b ≥ 60 . . . . . . earnings must be at least $60

__

Then the system of inequalities is ...

• m + b ≤ 15
• 3m + 5b ≥ 60