Question

Tickets for a choir concert cost $3 for students and $5 for adults. The choir director wants to sell at least $1,500 worth of tickets to this concert. She knows that 226 students purchased a ticket.

Enter the minimum number of adults that need to purchase a ticket to raise at least $1,500.
​

Answer 1

To determine the minimum number of adults that need to purchase a ticket, we begin by calculating the total revenue generated by the students.

Given that the cost of a student ticket is $3 and that 226 students purchased tickets, we can calculate the total revenue from student ticket sales as follows:

\[
\text{Revenue from students} = 226 \times 3 = 678 \text{ dollars}
\]

Next, we need to find out how much more money is needed to reach the minimum goal of $1,500. We do this by subtracting the revenue from students from the total target:

\[
\text{Additional revenue needed} = 1500 - 678 = 822 \text{ dollars}
\]

Now, let \( x \) represent the number of adult tickets sold. The price of an adult ticket is $5, so the revenue generated from adult ticket sales can be expressed as:

\[
\text{Revenue from adults} = 5x
\]

We need this revenue from adults to be at least $822:

\[
5x \geq 822
\]

To isolate \( x \), we divide both sides of the inequality by 5:

\[
x \geq \frac{822}{5} = 164.4
\]

Since \( x \) must be a whole number (as you cannot sell a fraction of a ticket), we round up to the nearest whole number:

\[
x \geq 165
\]

Therefore, the minimum number of adults that need to purchase a ticket is \( \boxed{165} \).