To solve this problem, we will set up a system of linear equations based on the given information.

Let:

• $a$ = price of an adult's ticket
• $c$ = price of a child's ticket

From the problem:

1. Three adults and four children pay $132: $3a + 4c = 132$
2. Two adults and three children pay $94: $2a + 3c = 94$

We are solving for $a$ and $c$. From the image, the price of a child's ticket is already provided as $c = 18$. Substituting $c = 18$ into both equations:

Substituting into the first equation:

$3a + 4(18) = 132$ $3a + 72 = 132$ $3a = 60 \quad \Rightarrow \quad a = 20$

Verifying in the second equation:

$2a + 3c = 94$ $2(20) + 3(18) = 94$ $40 + 54 = 94$ This is correct.

Final Answer:

• Price of a child's ticket: $\mathbf{\$18}$
• Price of an adult's ticket: $\mathbf{\$20}$

Would you like further details or have any questions?

Here are some related questions for practice:

1. How would the result change if the total for three adults and four children was $140 instead of $132?
2. How can you verify the solution using substitution and elimination methods?
3. What would happen if the equations were inconsistent (no solution)?
4. How can you generalize this approach to solve any system of two linear equations?
5. How would graphical methods show the solution to these equations?

Tip: Always double-check solutions by substituting them back into the original equations.