SOLUTION: Hello there, I have been struggling with this word problem. Would someone help me set up this word problem and also show me how to solve it. Thank you. "Jen Butler has been pricing

Question 664830: Hello there, I have been struggling with this word problem. Would someone help me set up this word problem and also show me how to solve it. Thank you. "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 adults ticket and the price of a child's ticket."
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
"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 adults ticket and the price of a child's ticket."
:
This is a typical two unknown, two equation problem, we can solve by elimination or substitution, whichever is easiest
:
let a = cost for an adult ticket
let c = cost for a child
:
write an equation for each statement
3a + 4c = 136
2a + 3c = 97
:
We will use elimination, mult the 1st equation by 2, mult the 2nd eq by 3
subtract the 1st equation from the 2nd equation
6a + 9c = 291
6a + 8c = 272
------------- subtraction eliminates a, find c
0 + c = 19
a child's ticket is $19
:
Find a using the 1st original equation: replace c with 19
3a + 4(19) = 136
:
You should be able to find a now, check your solutions in the original 2nd equation

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