Question

rob works part time at the fallbrook riding stable. He makes $5 an hour exercising horses and $10 hour cleaning stalls. Because Rob is a full time student he can work no more than 12 hours per week. however he must make $60 per week. write a system of inequalitites

Answer 1

Answer: 5x + 10y ≥ 60 ⇒ x+2y ≥ 12 .................. (i)

x + y ≤ 12 ................. (ii)

Step-by-step explanation:

Let the hours spent on exercising horse be x

Let the hours spent on cleaning stalls be y

According to question:

Rob can't work more than 12 hours. So eq. (i) will be x + y ≤ 12

Rob earns $5 an hour by exercising horses and $10 an hour cleaning stalls and he must make $60 . So eq. (ii) will be 5x + 10y ≥ 60.

Dividing eq. (ii) by 5, it will become x + 2y ≥ 12.

∴ system of inequalities are x + y ≤ 12 and x + 2y ≥ 12.

Answer 2

Let x be the number of hours exercising horses.
Let y be the number of hours cleaning stalls.

x + y <= 12
5x + 10y >= 60
x + 2y >= 12

At this point you might do well to graph this set of equations on Wolframalpha.com

In the meantime solve this system this way.

12 - x > y > 6 - x/2
When y =0 the x = 12.