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Answer :
To determine the maximum number of people who can go to the amusement park without spending more than [tex]$195 on parking and admission, let's break down the costs and set up an inequality.
1. Identify the Costs:
- Parking cost is a flat rate of $[/tex]9.75.
- Each ticket costs [tex]$17.75 per person, which includes tax.
2. Establish the Total Cost Formula:
The total cost for the group includes the parking fee and the combined cost of the tickets for everyone. If we let \( x \) represent the number of people, the formula for the total cost will be:
\[
\text{Total Cost} = \text{Parking Cost} + (\text{Ticket Cost per Person} \times \text{Number of People})
\]
\[
\text{Total Cost} = 9.75 + 17.75 \times x
\]
3. Set Up the Inequality:
The group can spend no more than $[/tex]195, so we set up the inequality:
[tex]\[
9.75 + 17.75 \times x \leq 195
\][/tex]
4. Solve the Inequality for [tex]\( x \)[/tex]:
To find the maximum number of people ([tex]\( x \)[/tex]) who can attend, you would solve this inequality. This step involves basic algebra: subtracting 9.75 from both sides and then dividing by 17.75.
By following these steps, we arrive at the answer:
[tex]\[
9.75 + 17.75 \times x \leq 195
\][/tex]
This inequality helps determine the maximum number of people who can attend the park together while staying within their budget of $195.
1. Identify the Costs:
- Parking cost is a flat rate of $[/tex]9.75.
- Each ticket costs [tex]$17.75 per person, which includes tax.
2. Establish the Total Cost Formula:
The total cost for the group includes the parking fee and the combined cost of the tickets for everyone. If we let \( x \) represent the number of people, the formula for the total cost will be:
\[
\text{Total Cost} = \text{Parking Cost} + (\text{Ticket Cost per Person} \times \text{Number of People})
\]
\[
\text{Total Cost} = 9.75 + 17.75 \times x
\]
3. Set Up the Inequality:
The group can spend no more than $[/tex]195, so we set up the inequality:
[tex]\[
9.75 + 17.75 \times x \leq 195
\][/tex]
4. Solve the Inequality for [tex]\( x \)[/tex]:
To find the maximum number of people ([tex]\( x \)[/tex]) who can attend, you would solve this inequality. This step involves basic algebra: subtracting 9.75 from both sides and then dividing by 17.75.
By following these steps, we arrive at the answer:
[tex]\[
9.75 + 17.75 \times x \leq 195
\][/tex]
This inequality helps determine the maximum number of people who can attend the park together while staying within their budget of $195.
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