Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $128. Two adults and three children must pay $91. Find the price of the adult's ticket and the price of a child's ticket.

Adults pay $20 while children pay $17

Step-by-step explanation:

Let price for adults be x while children be y

First case

Three adults and four children must pay $128

3x+4y=128

Second case

Two adults and three children must pay $91

2x+3y=91

To make x the subject

2x=91-3y

X=45.5-1.5y

Solving equations

By substituting x with 45.5-1.5y into

3x+4y=128

3(45.5-1.5y)+4y=128

136.5-4.5y+4y=128

0.5y=8.5

Y=2*8.5=17

X=45.5-(1.5*17)=20

Therefore, adults pay $20 while children pay $17