Let's break this down:

• Tom can work at most 25 hours per week.
• Job 1 pays $5 per hour.
• Job 2 pays $10 per hour.
• Tom needs to make at least $175 per week.

Let:

• $x$ be the number of hours Tom works at Job 1.
• $y$ be the number of hours Tom works at Job 2.

Constraints:

1. $x + y \leq 25$ (since he can work no more than 25 hours per week).
2. $5x + 10y \geq 175$ (since he needs to make at least $175).
3. $x \geq 0$ and $y \geq 0$ (he cannot work negative hours).

Solving the System:

The system of inequalities is:

x + y & \leq 25, \\ 5x + 10y & \geq 175, \\ x & \geq 0, \\ y & \geq 0. \end{aligned}$$ ### Step 1: Simplify the second inequality We can divide the second inequality $$5x + 10y \geq 175$$ by 5: $$x + 2y \geq 35.$$ ### Step 2: Analyze the system of inequalities The system becomes: $$\begin{aligned} x + y & \leq 25, \\ x + 2y & \geq 35, \\ x & \geq 0, \\ y & \geq 0. \end{aligned}$$ ### Step 3: Solve the system graphically or algebraically We can now solve for the values of $$x$$ and $$y$$ that satisfy both inequalities. - From $$x + y \leq 25$$, we get $$y \leq 25 - x$$. - From $$x + 2y \geq 35$$, we get $$y \geq \frac{35 - x}{2}$$. To find feasible solutions, we look for values of $$x$$ and $$y$$ that satisfy both these conditions. Would you like me to solve it further by finding specific values for $$x$$ and $$y$$? Here are some questions related to this scenario: 1. What would happen if Tom wanted to make more than $175 per week? 2. How would the solution change if Job 1 paid $8 per hour instead? 3. Can Tom work fewer hours if the wage at Job 2 increases? How? 4. How many hours would Tom need to work if he only worked Job 2 to make $175? 5. What is the maximum amount of money Tom can make in a week if he works the full 25 hours? **Tip**: In problems with multiple constraints, graphing inequalities can help you visualize the solution set.