Question

For the show choir's holiday performance, they are selling

tickets for $4.50 per student and $6.00 per adult. On the night of
their final performance, they collect $270 in ticket sales.

Answer 1

To determine the number of tickets sold for the show choir's holiday performance, we can set up a system of equations based on the given information. Let's assume that the number of student tickets sold is represented by 's' and the number of adult tickets sold is represented by 'a'.

According to the given information, each student ticket costs $4.50 and each adult ticket costs $6.00. The total amount collected from ticket sales is $270. We can express this information in the form of an equation:

4.50s + 6.00a = 270

Now, let's analyze the equation further to find a solution. We can start by simplifying it by dividing both sides of the equation by 0.50:

9s + 12a = 540

Next, we need to find a combination of 's' and 'a' that satisfies this equation. Since we don't have any additional information about the specific number of student or adult tickets sold, there are multiple possible solutions.

To find one possible solution, we can assume a value for either 's' or 'a' and solve for the other variable. Let's assume that all tickets sold were student tickets (s = 1) and solve for 'a':

9(1) + 12a = 540

9 + 12a = 540

12a = 540 - 9

12a = 531

a = 531 / 12

a ≈ 44.25

Since we cannot have a fraction of a ticket, this solution is not valid. However, it shows us that if all tickets were student tickets, we would fall short of collecting $270.

Let's try another assumption where all tickets sold were adult tickets (a = 1) and solve for 's':

9s + 12(1) = 540

9s + 12 = 540

9s = 540 - 12

9s = 528

s = 528 / 9

s ≈ 58.67

Again, we cannot have a fraction of a ticket, so this solution is not valid either. However, it shows us that if all tickets were adult tickets, we would exceed the target amount of $270.

From these two assumptions, we can conclude that there must be a combination of student and adult tickets sold to reach the target amount of $270. Unfortunately, without additional information or constraints, we cannot determine the exact number of student and adult tickets sold.

In conclusion, the number of student and adult tickets sold for the show choir's holiday performance cannot be determined with the given information alone.

Explanation:

Answer 2

Answer: $270 in ticket sales.

Explanation:

To find the number of student tickets and adult tickets sold, we can set up a system of equations based on the given information.

Let's assume the number of student tickets sold is "s" and the number of adult tickets sold is "a".

According to the problem, each student ticket costs $4.50, so the total amount collected from student tickets is 4.50.

Similarly, each adult ticket costs $6.00, so the total amount collected from adult tickets is 6.00a.

We are told that the total amount collected from ticket sales is $270, so we can set up the equation:

4.50s + 6.00a = 270

Now, we need to determine the possible values for "s" and "a" that satisfy this equation.

There are multiple solutions to this equation, so we need to find a combination of student and adult tickets that gives a total of $270.

Here's one possible solution:

If we assume 30 student tickets were sold (s = 30), then the total amount collected from student tickets would be 4.50 * 30 = $135.

Substituting this value into the equation, we have:

4.50s + 6.00a = 135 + 6.00a = 270

Solving for "a", we find:

6.00a = 270 - 135

6.00a = 135

a = 135 / 6.00

a ≈ 22.5

Since the number of adult tickets cannot be a decimal, we round down to the nearest whole number. Therefore, approximately 22 adult tickets were sold.

So, in this particular scenario, 30 student tickets and 22 adult tickets were sold to collect a total of $270 in ticket sales.