Question

Jen Butler has been pricing​ Speed-Pass train fares for a group trip to New York. Three adults and four children must pay

$ 83.  
Two adults and three children must pay
$ 59.  
Find the price of the​ adult's ticket and the price of a​ child's ticket.


The price of a​ child's ticket is
​$___

The price of the adult ticket is $___

Answer 1

a=adult pay
c=child pay
3a+4c=83
2a+3c=59
subtract
a+c=24
2a+2c=48
2a+3c-2a-2c=59-48
c=11
a=24-11=13
price of adult ticket=13$
price of child's ticket=$11

Answer 2

Let x and y represent the costs of adult and child tickets, respectively. Then the problem statement gives two relations:
.. 3x +4y = 83
.. 2x +3y = 59
A graph shows the solution to be (x, y) = (13, 11).

The price of a child's ticket is $11.
The price of the adult ticket is $13.