Question

A group of friends wants to go to the amusement park. They have no more than $155 to spend on parking and admission. Parking is $18, and tickets cost $24 per person, including tax. What is the maximum number of people who can go to the amusement park?

Answer 1

5

Explanation:

Define the variable:

• Let x be the number of people who can go to the amusement park.

Given information:

• Maximum amount to spend = $155
• Cost of parking = $18
• Cost of tickets per person = $24

Create an inequality using the defined variable and given information to model the scenario:

`\implies \textsf{Parking cost}+\textsf{Total ticket cost} \leq \textsf{Max amount available}`

`\implies 18 + 24x \leq 155`

To find the maximum number of people who can go to the amusement park, solve the inequality.

`\implies 18 + 24x-18 \leq 155-18`

`\implies 24x \leq 137`

`\implies (24x)/(24) \leq (137)/(24)`

`\implies x \leq 5.708333...`

As we cannot have part of a person, we need to round down to the nearest whole number.

Therefore, the maximum number of people who can go to the amusement park is 5.