To solve the problem of determining how many games Naomi can bowl given her budget, we need to establish an inequality based on the costs provided.
1. Identify the variables:
- Naomi’s total budget: \[tex]$18.00
- Cost of one game: \$[/tex]3.25
- Cost of shoe rental: \[tex]$1.50
2. Formulate the total cost equation:
- Naomi will rent shoes once, costing \$[/tex]1.50.
- Each game she plays costs \[tex]$3.25.
- Let \( x \) represent the number of games Naomi can bowl.
3. Create an expression for the total cost:
- The total cost includes the shoe rental and the cost for \( x \) games.
- Therefore, the total cost equation is given by:
\[
\text{Total cost} = 3.25 \cdot x + 1.50
\]
4. Set up the inequality:
- Since Naomi cannot spend more than \$[/tex]18.00, the total cost must be less than or equal to \[tex]$18.00. Hence, the inequality is:
\[
3.25 \cdot x + 1.50 \leq 18.00
\]
5. Review the given answer choices:
- A: \( 1.50 x + 3.25 \geq 18.00 \)
- This implies the total cost is more than or equal to \$[/tex]18.00, which is incorrect since Naomi cannot exceed her budget.
- B: [tex]\( 1.50 x + 3.25 \leq 18.00 \)[/tex]
- This incorrectly switches the coefficients for shoe rental and the cost per game and suggests a different relationship.
- C: [tex]\( 3.25 x + 1.50 \geq 18.00 \)[/tex]
- This again suggests a total cost that is more than or equal to \$18.00, which is also incorrect.
Thus, the correct inequality that can be used to solve for the number of games [tex]\( x \)[/tex] Naomi can bowl is:
[tex]\[ \boxed{3.25 \cdot x + 1.50 \leq 18.00} \][/tex]
This matches option C after confirming that it should use the “less than or equal to” ([tex]\(\leq\)[/tex]) relationship, thus none of the given options (A, B, C) directly reflects the necessary correct operation. Answer interpretation can be aligned to inevitably establish that correct inequality.
