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Step-by-step explanation:

let e be exercising hours

let c be cleaning stalls hours

Here is the inequality system per week:

Two possible solutions:

a) see attached graph

b) (2,8) (3,7)

Step-by-step explanation:

Part a

let x = number of hours exercising horses

let y = number of hours cleaning stalls

As he must earn at least $60 per week:   5x + 10y ≥ 60

As he can work no more than 12 hours per week:  x + y ≤ 12

Rearrange each equation to make y the subject:        

5x + 10y ≥ 60

⇒ 10y ≥ 60 - 5x

⇒ y ≥ 6 - (1/2)x

Therefore, graph the line    with a solid line, and shade above the line (shown in blue on the attached diagram)

x + y ≤ 12

⇒ y ≤ 12 - x

Graph the line    with a solid line, and shade below the line (shown in red on the attached diagram)

Part b

Possible solutions are any points found within the overlapping shaded region (shown in purple on the attached diagram) including the points on the lines:

e.g.  (2, 8) or (3, 7) or (4, 6) or (5, 5) or (5, 7) etc.

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step-by-step explanation: