Question

A group of friends wants to go to the amusement park. They have no more than $210 to spend on parking and admission. Parking is $5.75, and tickets cost $29.75 per person, including tax. Which inequality can be used to determine , the maximum number of people who can go to the amusement park?

Answer 1

Greetings from Brasil...

Be:

→ X = each person (each person pay 29.75)

→ assuming this group will only use 1 car to park, this group will pay 5.75 only once

So, Tickets + Parking must cost less than 210, otherwise there won't be enough money for group fun.

Then we can write:

29.75X + 5.75 ≤ 210

P.S. The maximum number of people allowed for this group will be:

29.75X ≤ 210 - 5.75

29.75X ≤ 204.25

X ≤ 204.25 ÷ 29.75

X ≤ 6.8

6 person × 29.75 = 178.5

178.5 + 5.75 = 184.25

If there are 6 people, there will be an exchange of 25.75

Answer 2

29.75x + 5.75 ≤ 210

Explanation:

Inequality symbols:

• < means "less than".
• > means "greater than".
• ≤ means "less than or equal to".
• ≥ means "greater than or equal to".

Given:

• Maximum amount to spend = $210
• Cost of parking = $5.75
• Cost of ticket = $29.75 per person (inc tax)
• Let x = maximum number of people.

Therefore, the total admission cost comprises the cost of a ticket per person plus the cost of parking:

⇒ 29.75x + 5.75

If the maximum amount of money to spend is $210, this means that the total cost is less than $210 or equal to $210. Therefore, we should use the ≤ symbol.

Therefore, the inequality that can be used to determine the maximum number of people who can go to the amusement park is:

• 29.75x + 5.75 ≤ 210