Question 132933
The Creekside Theater is putting on a play. The Hanson family bought 5 adult tickets and 2 children tickets for 129.00. The Rivera family bought 2 adult tickets and 6 children Tickets for 107.50.

(A) Write a system of equations to represent the situation.

(B) Then solve the system.  

(C) How much Does a Adult ticket cost and how much does a child ticket cost.

Let x = adult ticket

Let y = children ticket

We have a system of linear equations in two variables, the variables being x and y.

5x + 2y = 129.....Equation A

2x + 6y = 107.50...Equation B

The two equations above answer Part (A) of this question.

=========================================================

Part (B)

Solve the equation.

Let's use the addition method.

I want to do away with y and so, to do that I will multiply Equation A by -3.

Doing so, Equation A becomes:  -15x - 6y = -387...New Equation A.

We now add the New Equation A to the old Equation B to erase the y letter.

-15x - 6y = -387 PLUS 2x + 6y = 107.50, which becomes:

-13x = -279.5

To find the value of x, we divide both sides by -13.

x = -279.50/-13

x = 21.50

====================================================

To find y, I will plug the value of x just found into EITHER Equation A or B.

I will use the original Equation A but you can select any of the equations above.  Got it?

5x + 2y = 129...Equation A

5(21.50) + 2y = 129

107.50 + 2y = 129

2y = 129 - 107.50

2y = 21.50

y = 21.50/2

y = 10.75

We solve the equation in knowing that x = 21.50 and y = 10.75.

This means that the graphs of the two equations above meet at the point
(21.50, 10.75) when graphed on the xy-plane. The meeting place on the graph is the solution of this system of linear equations.
Is this clear?

========================

Part (C)

An adult ticket will cost $21.50.

A child ticket will cost $10.75.

How do I know that?  I found the value of x and y, right?  This is how I know the amount for the adult and child ticket.

Is this clear?