Jimmy brings $24 to the county fair for rides. Roller coaster rides cost $2, and the spinning cup rides cost $3. But Jimmy knows that he gets queasy if he takes more than 6 roller coaster rides or more than 8 spinning cup rides. Let r represent the number of roller coaster rides and let s represent the number of spinning cup rides.  In addition to r ≥ 0;s ≥ 0, which is a set of of inequalities that Jimmy can use to guide his choice of rides?  

To find a set of inequalities that guide Jimmy's choices, we need to consider the following:

1. **Budget Constraint**: Jimmy has $24 to spend on rides. The roller coaster ride costs $2, and the spinning cup ride costs $3. The total cost for `r` roller coaster rides and `s` spinning cup rides can be expressed as:
   \[
   2r + 3s \leq 24
   \]

2. **Maximum Ride Constraints**:
   - Jimmy can't take more than 6 roller coaster rides, so:
     \[
     r \leq 6
     \]
   - Jimmy can't take more than 8 spinning cup rides, so:
     \[
     s \leq 8
     \]

3. **Non-Negative Constraints**: Since the number of rides can't be negative:
   \[
   r \geq 0 \quad \text{and} \quad s \geq 0
   \]

### Summary of Inequalities:
The set of inequalities that Jimmy can use to guide his choice of rides is:

\[
\begin{aligned}
&2r + 3s \leq 24, \\
&r \leq 6, \\
&s \leq 8, \\
&r \geq 0, \\
&s \geq 0.
\end{aligned}
\]

These inequalities ensure that Jimmy stays within his budget and does not exceed his queasiness limits.

Would you like further explanation on any part of this, or do you have any other questions?

### Related Questions:
1. What is the maximum number of roller coaster rides Jimmy can take if he takes no spinning cup rides?
2. If Jimmy takes 4 roller coaster rides, how many spinning cup rides can he afford?
3. What combinations of rides exactly use up all of Jimmy's $24?
4. How would the inequalities change if the prices of the rides were different?
5. What would happen if Jimmy's budget increased to $30?

**Tip**: When solving inequalities, always check the feasible region by graphing the inequalities to visualize the solution space.

Jimmy brings $24 to the county fair for rides. Roller coaster rides cost $2, and the spinning cup rides cost $3. But Jimmy knows that he gets queasy if he takes more than 6 roller coaster rides or more than 8 spinning cup rides. Let r represent the number of roller coaster rides and let s represent the number of spinning cup rides. In addition to r ≥ 0; s ≥ 0, which is a set of inequalities that Jimmy can use to guide his choice of rides?

Explore how to set up inequalities to guide Jimmy's choice of rides at the fair. Learn to handle a budget constraint of $24 with roller coaster rides costing $2 and spinning cup rides costing $3, along with maximum ride limits. This problem is suitable for students in Grades 6-8 and covers linear inequalities and algebraic problem-solving.

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