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

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Question 1129052: Jen Butler has been pricing​ Speed-Pass train fares for a group trip 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 a​ child's ticket.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the price of an adult ticket
Let +b+ = the price of a child's ticket
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(1) +3a+%2B+4b+=+80+
(2) +2a+%2B+3b+=+57+
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Multiply both sides of (1) by +2+
Multiply both sides of (2) by +3+
Subtract (1) from (2)
(2) +6a+%2B+9b+=+171+
(1) +-6a+-+8b+=+-160+
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+b+=+11+
and
(2) +2a+%2B+33+=+57+
(2) +2a+=+24+
(2) +a+=+12+
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An adult ticket is $12
A child's ticket is $11
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check:
(1) +3%2A12+%2B+4%2A11+=+80+
(1) +36+%2B+44+=+80+
(1) +80+=+80+
OK