Question

y = children ticket $5
x + y = 12
$8x + 5y = 81
0.05x + 0.05 = 0.12(81)

Explanation:

Step1: Define Variables

Let \( x \) be adult tickets, \( y \) be children tickets. We have \( x + y = 12 \) (total tickets) and \( 8x + 5y = 81 \) (total cost).

Step2: Solve for \( y \) from first equation

From \( x + y = 12 \), we get \( y = 12 - x \).

Step3: Substitute into second equation

Substitute \( y = 12 - x \) into \( 8x + 5y = 81 \):
\( 8x + 5(12 - x) = 81 \)
\( 8x + 60 - 5x = 81 \)
\( 3x + 60 = 81 \)
\( 3x = 21 \)
\( x = 7 \)

Step4: Find \( y \)

Substitute \( x = 7 \) into \( y = 12 - x \):
\( y = 12 - 7 = 5 \)

Answer:

Adult tickets: \( \boldsymbol{7} \), Children tickets: \( \boldsymbol{5} \)