Question

The ball game took in 1,364 one Saturday. The number of $12 adult tickets was 17 more than twice the number of $5 child tickets. How many of each were sold?

Answer 1

- Let x represent the number of adult tickets that were sold.

- Let y represent the number of child tickets that were sold.

- The cost of an adult ticket is $12 and the cost of a child ticket is $5. The ball game sold $1,364 in tickets one Saturday. It means that:

12x + 5y = 1364

- The number of $12 adult tickets was 17 more than twice the number of $5 child tickets. It means that:

x = 17 + 2y

Then, substitute x in the first equation:

$12(17+2y)+5y=1364$

Simplify:

$\begin{gathered} 204+24y+5y=1364 \\ 204+29y=1364 \end{gathered}$

Solve for y:

$\begin{gathered} 204+29y-204=1364-204 \\ 29y=1160 \\ \frac{29y}{29}=\frac{1160}{29} \\ y=40 \end{gathered}$

Next, for x:

$x=17+2(40)=17+80=97$

Answer:

adult tickets = 97

child tickets = 40