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.

Question

Enter the minimum number of adults that need to purchase a ticket to raise at least $1,500.
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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 \( \boxed{165} \).