Question 132933: The creekside Theater is putting on a play.The hanson Family bought 5 adult ticketsand 2 child tickets for 129.00. The Rivera family bought 2 adult tickets and 6 cgild Tickets for 107.50.
Write a system of equations to represent the situation.
Then solve the system.How much Does a Adult ticket cost and how much does a child ticket cost.
Found 3 solutions by checkley71, vleith, nycsharkman:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! 5A+2C=129
2A+6C=107.50 NOW MULTIPLY THE FIRST EQUATION BY -3 & ADD THEM.
-15A-6C=-387
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-13A=-279.5
A=-279.5/-13
A=$21.50 COST OF THE ADULT TICKET.
5*21.5+2C=129
107.5+2C=129
2C=129-107.5
2C=21.5
C=21.5/2
C=$10.75 COST OF THE CHILDREN'S TICKET.
PROOF:
2*21.50+6*10.75=107.5
43+64.5=107.50
107.50=107.50
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website! Hanson 5A + 2C = 129.00
Riv 2A + 6C = 107.50
Multiply Hanson equation by 3 to yield
15A + 6C = 387
2A + 6C = 107.50
Subtract to get
13A = 279.50
A = 21.5 So adult tix cost 21.50 each
Now find child tix price
2 (21.50) + 6C = 107.50
6C = 64.50
C = 10.75 Child tix are 10.75 each
Check your answer by substiting these values for A and C back into the Hansons
Answer by nycsharkman(136) (Show Source):
You can put this solution on YOUR website! 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.
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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?
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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?
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