SOLUTION: For train tickets 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 c

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Question 1093745: For train tickets 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.
Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website!
3a + 4c = 136 multiply all sides times 2: 6a + 8c = 272 (1)
2a + 3c = 97 multiply all sides times 3 : 6a + 9c = 291 (2)
Subtract (2) from (1)
6a + 8c = 272
-
6a + 9c = 291
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0a -1c = -19
c = -19/-1 = 19 (remember -/- = +)
So the price of a child's ticket is 19
Let's substitute in one of the original equations. Any one, I'll use the second one:
2a + 3c = 97
2a + 3(19) = 97
2a = 97-3(19) = 40
a = 40/2 = 20 adult tickets are 20
Since we're at this, so you see that the result is the same with either equation:
3a + 4c = 136
3a + 4(19) = 136
3a + 76 = 136
3a = 60
a = 20
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Happy learning,
John