Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 132. Two adults and three children must pay $ 94. Find the price of the adult's ticket AND the price of a child's ticket.

Let a=price of adult ticket

let c=price of a child's ticket

start out by writing the following system of equations:

3a+4c=132

2a+3c=94

then, multiply the first equation by 2, and the second equation by 3 to get the following system of equations:

6a+8c=264

6a+9c=282

subtract the like terms to get the following equation:

-c=-18

divide both sides by - 1 to get rid of the negative to get the price of a child's ticket to be $18. to find the price of an adult ticket, pick one of the original equations to substitute the 18 in for c to find a. for example:

2a+3c=94

2a+3 (18) = 94

2a+54=94

-54 - 54

2a=40

2 2

a=20

or if you decide to use the other equation:

3a+4c=132

3a+4 (18) = 132

3a+72=132

-72 - 72

3a=60

3 3

a=20

either way, you still get an adults ticket to be $20 and a child's ticket to be $18.