Question

the theatre club sells a total of 101 tickets to its first play. A student ticket cost 1 dollar. An adult ticket costs 2.50 dollars. Total ticket sales are 164 dollars how many students tickets are sold

Answer 1

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

We can set up the following equations based on the information provided:

1. The total number of tickets sold:
\[
x + y = 101
\]

2. The total revenue from ticket sales:
\[
1x + 2.5y = 164
\]

Now, we can solve these equations step by step.

First, let's solve for \( y \) in terms of \( x \) using the first equation:
\[
y = 101 - x
\]

Next, substitute this expression for \( y \) into the second equation:
\[
1x + 2.5(101 - x) = 164
\]

Distributing the 2.5:
\[
x + 252.5 - 2.5x = 164
\]

Combining like terms:
\[
-1.5x + 252.5 = 164
\]

Now, isolate \( x \):
\[
-1.5x = 164 - 252.5
\]
\[
-1.5x = -88.5
\]
\[
x = \frac{-88.5}{-1.5} = 59
\]

Thus, the number of student tickets sold is \( x = 59 \).

Now, let's find \( y \):
\[
y = 101 - x = 101 - 59 = 42
\]

To verify, we can check the total ticket sales:
\[
1(59) + 2.5(42) = 59 + 105 = 164
\]

Both conditions (total tickets and total sale amount) are satisfied.

Therefore, the number of student tickets sold is \( \boxed{59} \).