Question

Tickets to a movie cost 5$ for adults and 3$ for students. A group of friends purchased 18 tickets for $82.00. How many Adults ticket did they buy?

Answer 1

Let's use algebra to solve this problem.

Let \( x \) be the number of adult tickets and \( y \) be the number of student tickets.

We have two equations based on the information given:

1. The total number of tickets purchased:
\[
x + y = 18
\]

2. The total cost of the tickets:
\[
5x + 3y = 82
\]

Now we can solve these equations step by step.

From the first equation, we can express \( y \) in terms of \( x \):
\[
y = 18 - x
\]

Now we can substitute \( y \) into the second equation:
\[
5x + 3(18 - x) = 82
\]

Distribute the 3:
\[
5x + 54 - 3x = 82
\]

Combine like terms:
\[
2x + 54 = 82
\]

Subtract 54 from both sides:
\[
2x = 28
\]

Now divide by 2:
\[
x = 14
\]

So, the number of adult tickets purchased is \( \boxed{14} \).

To check, we can find \( y \):
\[
y = 18 - x = 18 - 14 = 4
\]

Now let's verify the total cost:
\[
5(14) + 3(4) = 70 + 12 = 82
\]

The calculations confirm that the solution is correct. Thus, they bought **14 adult tickets**.