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 inequalities.

Answer. Rob works part-time at the Fallbrook Riding Stable, balancing his job with his studies. He earns:

• $5 per hour exercising horses
• $10 per hour cleaning stalls

Since he is a full-time student, he has limited availability and can work at most 12 hours per week. Additionally, he must make at least $60 per week to meet his financial needs.

Step 1: Define Variables

Let:

• $x$ = hours Rob spends exercising horses
• $y$ = hours Rob spends cleaning stalls

Step 2: Write the Constraints

Time Constraint

Rob can work at most 12 hours per week, so:

$$x+y\le 12$$

Earnings Constraint

Rob earns:

• $5 per hour exercising horses → total earnings from this = $5x$
• $10 per hour cleaning stalls → total earnings from this = $10y$
  He must earn at least $60 per week, so:

$$5x+10y\ge 60$$

Non-Negative Work Hours

Rob cannot work negative hours, so:

$$x\ge 0,y\ge 0$$

Final System of Inequalities:

$$x+y\le 12$$ $$5x+10y\ge 60$$ $$x\ge 0,y\ge 0$$

This system represents all of Rob’s work constraints!