SOLUTION: 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.â€

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Question 1178546: 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​ adult's ticket and the price of a​ child's ticket.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

Was solved long time ago at this forum under this link

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.664830.html

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.664830.html


E N J O Y (!)



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


There are of course many paths to a solution of this problem using formal algebra.

Here is an unusual path that makes solving this particular problem easy, because of exactly how the given information is presented. We have

(1) 3a+4d=136
(2) 2a+3d=97

A typical solution using elimination would have you multiply the first equation by 2 and the second by -3, then adding the two resulting equations to eliminate a.

But there is a faster and easier path to the solution of this particular pair of equations.

Compare the two given equations:
(3) a+d=39

double that:
(4) 2a+2d=78

Compare (4) and (2):
d=19

Plug that into (3) to find a=20.

ANSWER: Adult fare $20; child fare $19.

CHECK:
3(20)+4(19)=60+76=136
2(20)+3(19)=40+57=97