SOLUTION: Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusment park. Max's family spent $146 on 3 adult tickets and 2 youth tickets. What is the price of a youth

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusment park. Max's family spent $146 on 3 adult tickets and 2 youth tickets. What is the price of a youth      Log On


   

Question 391393: Brianna's family spent $134 on 2 adult tickets and 3 youth tickets at an amusment park. Max's family spent $146 on 3 adult tickets and 2 youth tickets. What is the price of a youth ticket?
Found 2 solutions by ewatrrr, rfer:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

This question Sets Up two equations with 2 unknowns        

Let x and y represent the cost of the youth and adult ticket respectively

Question states***

 3x + 2y = $134   

 2x + 3y = $146

using elimination to solve for x

 9x +6y = 3*134    | Multiplying 1st equation by 3

-4x -6y = -2*146   | Multiplying 2nd equation by -2



    5x = 3*134 - 2*146

    5x = $110

     x = $22,  the cost of the youth ticket



CHECKING our Answer*** ($34 being the cost of the adult ticket) y = (134-3*22)/2

  3*$22 + 2*$34 = $66 + $68 = $134

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
3y+2a=134 a=67-1.5y
2y+3a=146
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2y+3(67-1.5y)=146
2y+201-4.5y=146
-2.5y=-55
y=22 tickets
------------------
2(22)+3a=146
3a=102
a=34 tickets