Answer :
Let's work through the problem step by step to determine which inequality can be used to find [tex]\( x \)[/tex], the maximum number of people who can go to the amusement park.
1. Understand the Costs:
- Parking Cost: \[tex]$9.75 (This is a one-time cost regardless of how many people go.)
- Ticket Cost per Person: \$[/tex]17.75 (Each person needs a ticket.)
2. Total Budget: The total amount they can spend is no more than \$195.
3. Set Up the Inequality:
To find out how many people [tex]\( x \)[/tex] can go, consider the combined cost of the parking and the tickets for [tex]\( x \)[/tex] people. The inequality representing this situation is:
[tex]\[
\text{parking cost} + (\text{ticket cost per person} \times \text{number of people}) \leq \text{total budget}
\][/tex]
Here, the inequality is:
[tex]\[
9.75 + 17.75x \leq 195
\][/tex]
4. Rearrange the Inequality to Solve for [tex]\( x \)[/tex]:
Subtract the parking cost from both sides:
[tex]\[
17.75x \leq 195 - 9.75
\][/tex]
Simplify the right side:
[tex]\[
17.75x \leq 185.25
\][/tex]
Divide both sides by 17.75 to solve for [tex]\( x \)[/tex]:
[tex]\[
x \leq \frac{185.25}{17.75}
\][/tex]
5. Find the Maximum Number of People:
When you calculate [tex]\( \frac{185.25}{17.75} \)[/tex], you get a numerical result, which, when rounded down, will give the maximum whole number of people that can go to the amusement park.
So, the correct inequality to determine the maximum number of people who can go is:
[tex]\[
9.75 + 17.75x \leq 195
\][/tex]
And from performing the calculation, without rounding too early, you can determine exactly how many people can go given their budget constraints.
1. Understand the Costs:
- Parking Cost: \[tex]$9.75 (This is a one-time cost regardless of how many people go.)
- Ticket Cost per Person: \$[/tex]17.75 (Each person needs a ticket.)
2. Total Budget: The total amount they can spend is no more than \$195.
3. Set Up the Inequality:
To find out how many people [tex]\( x \)[/tex] can go, consider the combined cost of the parking and the tickets for [tex]\( x \)[/tex] people. The inequality representing this situation is:
[tex]\[
\text{parking cost} + (\text{ticket cost per person} \times \text{number of people}) \leq \text{total budget}
\][/tex]
Here, the inequality is:
[tex]\[
9.75 + 17.75x \leq 195
\][/tex]
4. Rearrange the Inequality to Solve for [tex]\( x \)[/tex]:
Subtract the parking cost from both sides:
[tex]\[
17.75x \leq 195 - 9.75
\][/tex]
Simplify the right side:
[tex]\[
17.75x \leq 185.25
\][/tex]
Divide both sides by 17.75 to solve for [tex]\( x \)[/tex]:
[tex]\[
x \leq \frac{185.25}{17.75}
\][/tex]
5. Find the Maximum Number of People:
When you calculate [tex]\( \frac{185.25}{17.75} \)[/tex], you get a numerical result, which, when rounded down, will give the maximum whole number of people that can go to the amusement park.
So, the correct inequality to determine the maximum number of people who can go is:
[tex]\[
9.75 + 17.75x \leq 195
\][/tex]
And from performing the calculation, without rounding too early, you can determine exactly how many people can go given their budget constraints.
