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?

NOTE: Type the correct numerical value into the blank to receive credit for this question.

(1 point)
adult tickets

Answer 1

To find the number of adult tickets sold, we can use the equation given:

\[
10.50a + 3.75b = 2071.50
\]

We know that \( b = 82 \) since 82 students attended. Let's substitute \( b \) into the equation:

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

Now we will calculate \( 3.75 \times 82 \):

\[
3.75 \times 82 = 307.50
\]

Now, substitute this value back into the equation:

\[
10.50a + 307.50 = 2071.50
\]

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

\[
10.50a = 2071.50 - 307.50
\]

Calculating the right side:

\[
2071.50 - 307.50 = 1764.00
\]

Now we have:

\[
10.50a = 1764.00
\]

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

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

Calculating \( a \):

\[
a = 168
\]

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