During the summer, you want to earn at least $150 per week. You can earn $10 per hour working for a farmer and $5 per hour babysitting. You can work at most 25 hours per week.

1. Write a system of linear inequalities that models the situation.
2. Solve your system, and determine how many hours per week you would work babysitting.
3. If you work 10 hours per week on the farm and 12 hours per week babysitting, will you meet your goal?

you can work only as a farmer 15 hours per week 10x+5y>=150 => 10 x >= 150- 5y :5 => 2x >=30-y => 30-2x <= y x+y<= 25 => y>=30-2x y<=25-x

Answered by dannielle | 2024-06-10

x = nr. hrs working for a farmer; y = nr. hrs. babysitting; x + y <= 25; 10x + 5y >= 150
a) Solve the system => one of the solution is x =5; y = 20(babysitting) b) 10 + 12 =22 <= 25; 10*10 + 5*12 = 160 >=150.

Answered by crisforp | 2024-06-10

The system of inequalities that models the situation is 10x + 5y ≥ 150 and x + y ≤ 25, with both variables being non-negative. The combination of working 10 hours on the farm and 12 hours babysitting achieves an income of $160, which meets the goal of at least $150. Therefore, the student's plan is successful in reaching their financial target.
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Answered by dannielle | 2024-09-05