Question

A group of friends wants to go to the amusement park. They have no more than $110 to spend on parking and admission. Parking is $17.75, and tickets cost $20.50 per person, including tax. Write and solve an inequality that can be used to determine xx, the number of people who can go to the amusement park.

Answer 1

To determine how many individuals can attend the amusement park within a $110 budget, we create the inequality 17.75 + 20.50x <= 110 (where x is the number of people) and solve for x to find that a maximum of 4 people can go without exceeding the budget.

Step-by-step explanation:

To determine the number of people who can go to the amusement park without exceeding the budget, we can set up and solve an inequality. The total amount of money available is $110, parking costs $17.75, and each ticket is $20.50 per person. We let x represent the number of people.

The inequality to represent this situation is:

17.75 + 20.50x ≤ 110

To solve for x, we subtract the parking cost from the total budget and then divide by the cost per ticket:

(110 - 17.75) / 20.50 ≤ x

This gives us:

92.25 / 20.50 ≤ x

Therefore, the number of people that can go without exceeding the budget is:

x ≤ 4.5

Since we cannot have half a person, the maximum number of people is 4.

Answer 2

Inequality: 20.50x + $17.75 ≤ $110

Solve: 4 people can go to the amusement park

Explaination:

Inequality:

$110 = Amount of money they have

$17.75 = Parking Cost

$20.50 = Cost of tickets per person

Because they only have $110, they can't spend more than that amount.

Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (aka x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:

20.50x + $17.75 ≤ $110

Solve:

$110 - $17.75 = $92.25 (92.25 is how much is left for tickets after subtracting the parking cost)

$20.50 x 4 = $82 (4 tickets can be bought for the price of $20.50)

$92.25 - $82 = $10.25 (10.25 isn't enough for another person)

So, the solution to the inequality is 4 people can go to the amusement park.