SOLUTION: Jen Butler has been pricing Speed-Pass train fares for a group to New York. Three adults and four children must pay $80. Two adults and three children must pay $57. Find the price

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Question 1095303: Jen Butler has been pricing Speed-Pass train fares for a group to New York. Three adults and four children must pay $80. Two adults and three children must pay $57. Find the price of the adult’s ticket and the price of the child’s ticket.
Answer by ikleyn(52900) About Me  (Show Source):
You can put this solution on YOUR website!
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3a + 4c = 80,   (1)
2a + 3c = 57.   (2)


Let us solve it using the Elimination method.


Multiply eq(1) by 2 (both sides. Multiply eq(2) by 3. You will get

6a + 8c = 160,   (3)
6a + 9c = 171.   (4)


Now subtract eq(3) from eq(4). You will get

c = 171 - 160 = 11.


Thus the children ticket costs $11.


Then from eq(2), the adult tickets costs  %2857-3%2A11%29%2F2 = $12.


Please check it on your own.