SOLUTION: Jen Butler has been pricing speed-pass train fares for a group trip to New York. Three adults and four children must pay $108. Two adults and three children must pay $76. Find the

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Question 1022023: Jen Butler has been pricing speed-pass train fares for a group trip to New York. Three adults and four children must pay $108. Two adults and three children must pay $76. Find the price of the adults 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's ticket
Let +b+ = the price of a child's ticket
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(1) +3a+%2B+4b+=+108+
(2) +2a+%2B+3b+=+76+
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Multiply both sides of (1) by +2+
Multiply both sides of (2) by +3+
Subtract (1) from (2)
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(2) +6a+%2B+9b+=+228+
(1) +-6a+-+8b+=+-216+
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+b+=+12+
and
(1) +3a+%2B+4b+=+108+
(1) +3a+%2B+4%2A12+=+108+
(1) +3a+%2B+48+=+108+
(1) +3a+=+60+
(1) +a+=+20+
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The price of an adult's ticket is $20
The price of a child's ticket is $12
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check:
(2) +2a+%2B+3b+=+76+
(2) +2%2A20+%2B+3%2A12+=+76+
(2) +40+%2B+36+=+76+
(2) +76+=+76+
OK