Question 1176912
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Jen Butler has been pricing speed-pass train fares for a group trip to New York. 
Three adults and four children must pay $136. Two adults and three children must pay $97. 
Find the price of the adult's ticket and the price of the child's ticket.
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From the condition, you have these two equations


    3A + 4C = 136

    2A + 3C =  97.


To find A and C, use the determinant method (= Cramer's rule)


    A = {{{(136*3 - 97*4)/(3*3 - 2*4)}}} = 20 dollars for each adult tickets

    C = {{{(3*97 - 2*136)/(3*3 - 2*4)}}} = 19 dollars for each child's ticket.
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Solved.