Question

Richard took a group of friends and their kids to see a Star Wars movie in 3D. He bought a total of 20 tickets. Adult movie tickets were $12 and children's tickets were $8. If the total cost of the tickets was $192, how many children's tickets did Richard buy?

Answer 1

Data:

Total tickets: 20

Adult movie tickets: A

Children's tickets: C

A: $12

C: $8

As the total number of tickets is 20 you have the next.

$A+C=20$

As the total cost of the tickets is $192 you have the next:

$12A+8C=192$

Then, you have the next system of equations:

$\begin{gathered} A+C=20 \\ 12A+8C=192 \end{gathered}$

To solve a system of equations:

1. Solve one of the variables in one of the equations:

Solve A in the first equation:

$A=20-C$

2. Use the value of A you get in the first part in the other equation:

$12(20-C)+8C=192$

3. Solve C:

- Remove parenthesis. Distributive property:

$240-12C+8C=192$

- Combine like terms:

$240-4C=192$

- Substract 240 in both sides of the eqaution:

$\begin{gathered} 240-240-4C=192-240 \\ \\ -4C=-48 \end{gathered}$

-Divide both sides of the equation into -4:

$\begin{gathered} \frac{-4}{-4}C=\frac{-48}{-4} \\ \\ C=12 \end{gathered}$

As C is 12. Richard bought 12 Children's tickets