Answer :
To determine how many people can attend the amusement park within the budget constraints, we need to set up an inequality.
1. Identify the costs and the budget:
- Cost of parking: \[tex]$11.50 - Cost per ticket per person: \$[/tex]39
- Total budget available: \[tex]$295 2. Express the total cost in terms of the number of people, \( x \): - The total cost includes parking and the sum of ticket costs for \( x \) people. - Therefore, the total cost is \( 39x + 11.5 \). 3. Set up the inequality to ensure the total cost does not exceed the budget: - The group of friends wants to ensure that they do not spend more than \$[/tex]295.
- The inequality representing this constraint is:
[tex]\[ 39x + 11.5 \leq 295 \][/tex]
4. Identify the correct format for the inequality:
- Rearrange [tex]\( 39x + 11.5 \leq 295 \)[/tex] to compare it with the given options.
- The inequality correctly states that the total cost (comprised of ticket costs and parking) should be less than or equal to \$295.
5. Select the appropriate inequality from the provided options:
- The correct inequality that represents this situation is:
[tex]\[ 295 \geq 39x + 11.5 \][/tex]
Thus, the inequality that can be used to determine [tex]\( x \)[/tex], the maximum number of people who can go to the amusement park, is:
[tex]\[ 295 \geq 39x + 11.5 \][/tex]
1. Identify the costs and the budget:
- Cost of parking: \[tex]$11.50 - Cost per ticket per person: \$[/tex]39
- Total budget available: \[tex]$295 2. Express the total cost in terms of the number of people, \( x \): - The total cost includes parking and the sum of ticket costs for \( x \) people. - Therefore, the total cost is \( 39x + 11.5 \). 3. Set up the inequality to ensure the total cost does not exceed the budget: - The group of friends wants to ensure that they do not spend more than \$[/tex]295.
- The inequality representing this constraint is:
[tex]\[ 39x + 11.5 \leq 295 \][/tex]
4. Identify the correct format for the inequality:
- Rearrange [tex]\( 39x + 11.5 \leq 295 \)[/tex] to compare it with the given options.
- The inequality correctly states that the total cost (comprised of ticket costs and parking) should be less than or equal to \$295.
5. Select the appropriate inequality from the provided options:
- The correct inequality that represents this situation is:
[tex]\[ 295 \geq 39x + 11.5 \][/tex]
Thus, the inequality that can be used to determine [tex]\( x \)[/tex], the maximum number of people who can go to the amusement park, is:
[tex]\[ 295 \geq 39x + 11.5 \][/tex]
