Answer :
To determine the maximum number of people (`x`) who can go to the amusement park, we need to establish an inequality for the total cost, which should not exceed [tex]$195.
1. Parking Cost: The parking fee for the group is fixed at $[/tex]9.75.
2. Ticket Cost per Person: Each person needs a ticket costing [tex]$17.75.
3. Formulate the Inequality:
- The total cost is the sum of the parking cost and the ticket costs for `x` people.
- Therefore, the expression for the total cost is: \( \text{Parking cost} + \text{Cost per person} \times \text{Number of people} \).
- Plugging in the values, the expression becomes: \( 9.75 + 17.75 \times x \).
4. Set Up the Inequality:
- Since the total cost must be no more than $[/tex]195, our inequality is:
[tex]\[
9.75 + 17.75 \times x \leq 195
\][/tex]
5. Solution Form:
- The inequality can be rearranged to focus on `x`:
[tex]\[
195 \geq 9.75 + 17.75 \times x
\][/tex]
This inequality will help us find the maximum number of people who can attend the amusement park without exceeding the total budget of $195.
1. Parking Cost: The parking fee for the group is fixed at $[/tex]9.75.
2. Ticket Cost per Person: Each person needs a ticket costing [tex]$17.75.
3. Formulate the Inequality:
- The total cost is the sum of the parking cost and the ticket costs for `x` people.
- Therefore, the expression for the total cost is: \( \text{Parking cost} + \text{Cost per person} \times \text{Number of people} \).
- Plugging in the values, the expression becomes: \( 9.75 + 17.75 \times x \).
4. Set Up the Inequality:
- Since the total cost must be no more than $[/tex]195, our inequality is:
[tex]\[
9.75 + 17.75 \times x \leq 195
\][/tex]
5. Solution Form:
- The inequality can be rearranged to focus on `x`:
[tex]\[
195 \geq 9.75 + 17.75 \times x
\][/tex]
This inequality will help us find the maximum number of people who can attend the amusement park without exceeding the total budget of $195.
