Question 1178546
<br>
There are of course many paths to a solution of this problem using formal algebra.<br>
Here is an unusual path that makes solving this particular problem easy, because of exactly how the given information is presented.  We have<br>
(1) 3a+4d=136
(2) 2a+3d=97<br>
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.<br>
But there is a faster and easier path to the solution of this particular pair of equations.<br>
Compare the two given equations:
(3) a+d=39<br>
double that:
(4) 2a+2d=78<br>
Compare (4) and (2):
d=19<br>
Plug that into (3) to find a=20.<br>
ANSWER: Adult fare $20; child fare $19.<br>
CHECK:
3(20)+4(19)=60+76=136
2(20)+3(19)=40+57=97<br>