Question

Jillian's school is selling tickets for a play. The ticket cost is $10.50 for adults and $3.75 for students. The ticket sales for opening night totaled $2071.50. The equation 10.50a+3.75b=2071.50
, where a is the number of adult tickets sold and b is the number of student tickets sold, can be used to find the number of adult and student tickets. If 82 students attended, how many adult tickets were sold?

Answer 1

To find out how many adult tickets were sold, we can use the given equation:

\[
10.50a + 3.75b = 2071.50
\]

where:
- \( a \) is the number of adult tickets sold,
- \( b \) is the number of student tickets sold, and
- we know that \( b = 82 \) (the number of student tickets sold).

Now, we substitute \( b \) into the equation:

\[
10.50a + 3.75(82) = 2071.50
\]

Calculating \( 3.75 \times 82 \):

\[
3.75 \times 82 = 307.50
\]

Now, substitute this value back into the equation:

\[
10.50a + 307.50 = 2071.50
\]

Next, we isolate \( a \) by subtracting \( 307.50 \) from both sides:

\[
10.50a = 2071.50 - 307.50
\]

Calculating the right side:

\[
10.50a = 1764.00
\]

Now, divide both sides by \( 10.50 \) to solve for \( a \):

\[
a = \frac{1764.00}{10.50}
\]

Calculating the division:

\[
a = 168
\]

Thus, the number of adult tickets sold is \( \boxed{168} \).