Get ready for an amusement park day of fun! You and your family want to spend the day at a theme park. You have pooled your money together and have $685. The tickets to the park are $125 each and there is an online processing fee of $5.75 per ticket. You also need to pay $20 for parking. If you have a family of five, do you have enough money to purchase these tickets? Find an inequality to determine how many tickets can be purchased. Then find how many tickets you are able to purchase based on your inequality.
Let's assume x as the number of tickets to be purchased.
The cost of one ticket is $125 and the online processing fee is $5.75, so the total cost per ticket is $125 + $5.75 = $130.75.
The total cost of x tickets is x * $130.75 = $130.75x.
Additionally, we need to pay $20 for parking.
The total cost of the day at the theme park, including tickets and parking, is $130.75x + $20.
We have $685 to spend.
Therefore, the inequality representing the number of tickets we can purchase is:
$130.75x + $20 ≤ $685.
To find how many tickets we can purchase, we need to solve the inequality:
$130.75x + $20 ≤ $685.
Let's solve it:
$130.75x ≤ $685 - $20
$130.75x ≤ $665
x ≤ $665 / $130.75
x ≤ 5.08
We cannot purchase a fraction of a ticket, so the maximum number of tickets we can buy is 5.
Therefore, the family can purchase a maximum of 5 tickets based on the given budget.