Question

The Lyncrest School PTO is holding their annual Halloween Bash to benefit the 4th grade

graduating class. The cost of admission is $5 per person, and 210 people pre-registered to attend
During the pre-sale, they sold 52 ticket packages for $25 each, 45 tricky tray packages for $20
each, and 60 50/50 raffle ticket packages for $15 each. The PTO will be selling ticket packages at
the door on the night of the Bash for $30 each. Additionally, they have to pay $325 for the DJ and
$700 for the decorations and supplies.
A. If the goal is to profit at least $4,000 for the class, what is the minimum number of ticket
packages that must be sold at the door on the night of the Bash? Write and solve an
inequality to find the answer. Don't forget to define your variable, and show all your work!
B. The actual amount of money profited for the 4th grade class was $5,975. How many ticket
packages were sold at the door on the night of the Bash?

Answer 1

A. 30 B. 95 Packages.

Explanation:

A. The total income from the pre-sale is calculated as follows:

Admission: $5/person * 210 people = $1050

Ticket packages: $25/package * 52 packages = $1300

Tricky tray packages: $20/package * 45 packages = $900

Raffle ticket packages: $15/package * 60 packages = $900

So, the total pre-sale income is $1050 + $1300 + $900 + $900 = $4150.

The total expenses for the DJ and decorations are $325 + $700 = $1025.

The profit from the pre-sale, subtracting the expenses from the income, is $4150 - $1025 = $3125.

If the goal is to profit at least $4000, the income from the ticket packages sold at the door must be at least $4000 - $3125 = $875.

Let’s define the variable x as the number of ticket packages sold at the door. Each package is sold for $30, so the inequality to solve is $30x >= $875.

Solving for x gives x >= $875 / $30 ≈ 29.17. Since we can’t sell a fraction of a ticket, we need to round up to the nearest whole number. So, the minimum number of ticket packages that must be sold at the door is 30.

B. If the actual profit was $5975, and we know that $3125 was made in the pre-sale, then the income from the door sales is $5975 - $3125 = $2850.

Since each ticket package sold at the door is $30, the number of packages sold is $2850 / $30 = 95 packages. So, 95 ticket packages were sold at the door on the night of the Bash.