Question

Need help with Systems of 2 Equations Word Problems . Problem 3.

Answer 1

We are told that a theater have sold 6 adult tickets and 3 child tickets for a total of 96. If "x" is the price for adult and "y" the price for children, then we can describe the situation mathematically as:

`6x+3y=96,(1)`

Now we are told that there were sold 8 adult tickets and 2 children tickets for a total of 112. This can be represented mathematically as:

`8x+2y=112,(2)`

This gives us a system of two equation with two variables. To solve the system we will use the method of subtitution. First, we will solve for "y" in equation (1):

`6x+3y=96`

Subtracting 6x to both sides:

`3y=96-6x`

Dividing both sides by 3:

`\begin{gathered} y=(96)/(3)-(6)/(3)x \\ y=32-2x \end{gathered}`

Then we will replace this value of "y" in equation (2):

`8x+2(32-2x)=112`

Using the distributive property:

`8x+64-4x=112`

Adding like terms:

`4x+64=112`

Subtracting 64 to both sides:

`4x=112-64`

Solving the operation:

`4x=48`

Dividing both sides by 4:

`x=(48)/(4)=12`

Therefore, x = 12. Replacing this value in equation (1):

`y=32-2(12)`

Solving the operations:

`y=8`

Therefore, adult tickets cost $12 and children tickets cost $8.