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A group of friends wants to go to the amusement park. They have no more than [tex]$\$295$[/tex] to spend on parking and admission. Parking is [tex]$\[tex]$11.50$[/tex][/tex], and tickets cost [tex]$\$39$[/tex] per person, including tax. Which inequality can be used to determine [tex]$x$[/tex], the maximum number of people who can go to the amusement park?

A. [tex]295 \leq 39x + 11.5[/tex]
B. [tex]295 \geq 39x + 11.5[/tex]
C. [tex]295 \geq 39(x + 11.5)[/tex]
D. [tex]295 \leq 39(x + 11.5)[/tex]



Answer :

GinnyAnswer
Let's break down the problem step by step to determine the appropriate inequality for finding the maximum number of people, [tex]\( x \)[/tex], who can go to the amusement park.

1. Identify the total money available:
The group has a maximum amount of [tex]$295. 2. Identify the costs involved: - Parking cost is $[/tex]11.50.
- The cost of a ticket per person is [tex]$39. 3. Set up the cost equation: The total cost will be the sum of the parking cost and the cost of tickets for \( x \) number of people. Parking cost: $[/tex]11.50

Ticket cost for [tex]\( x \)[/tex] people: [tex]$39x Therefore, the total cost for \( x \) people can be expressed as: \[ 39x + 11.5 \] 4. Set up the inequality: Since the group cannot spend more than $[/tex]295, the total cost must be less than or equal to $295. This can be written as:
[tex]\[ 39x + 11.5 \leq 295 \][/tex]

Rewriting this inequality, it becomes:
[tex]\[ 295 \geq 39x + 11.5 \][/tex]

Therefore, the correct inequality that can be used to determine the maximum number of people who can go to the amusement park, [tex]\( x \)[/tex], is:
[tex]\[ 295 \geq 39x + 11.5 \][/tex]

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