Use the fact that 250 tickets were sold in total to make one equation, and use the total amount of money collected ($2410) with the ticket prices to make another equation.

Try solving one of the equations for a variable (like $a = 250 - c$) and substitute it into the other equation so you have just one variable to solve for.

After you solve the system, check whether your solution gives the number of child tickets or adult tickets, and make sure you answer with the correct one.

In Desmos, enter the two equations in terms of $a$ (adult tickets) and $c$ (child tickets) by rewriting them with $c$ as $y$ and $a$ as $x$:

• Type y = 250 - x for $a + c = 250$.
• Type y = (2410 - 12x)/7 for $12a + 7c = 2410$.

Look for the point where the two lines intersect. The $y$-coordinate of this intersection represents the number of child tickets, and the $x$-coordinate represents the number of adult tickets. Use the $y$-value as your final answer.

Let $a$ be the number of adult tickets and $c$ be the number of child tickets.

From the problem:

• Total tickets: $a + c = 250$.
• Total money: $12a + 7c = 2410$.

From $a + c = 250$, solve for $a$:

Substitute this into the money equation $12a + 7c = 2410$:

Distribute and combine like terms:

Subtract 3000 from both sides:

Divide both sides by $-5$:

Evaluate the last expression to get $c = 118$. The variable $c$ represents the number of child tickets, so the theater sold 118 child tickets. (Answer choice C.)