SOLUTION: Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 92. Two adults and three children must pay $65. Find t

Algebra ->  Graphs -> SOLUTION: Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 92. Two adults and three children must pay $65. Find t      Log On


   

Question 1143483: Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 92. Two adults and three children must pay $65. Find the price of the​ adult's ticket and the price of a​ child's ticket.
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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From the condition, you have these two equations


    3a + 4c = 92    (1)

    2a + 3c = 65    (2)


To solve it, multiply eq(1) by 2 and multiply eq(2) by 3.  You will get


    6a + 8c = 2*92     (1')

    6a + 9c = 3*65     (2')


Now subtract eq(1') from eq(2').  You will get


    c  = 3*65 - 2*92 = 11.


To find "a", substitute  c= 11 into equation (1)

    3a + 4*11 = 92

    3a = 92 - 44

    3a = 48

     a = 48/3 = 16.


ANSWER.  Adult's ticket price is $16;  child's ticket price is $11.