Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $ 104. Two adults and three children must pay $ 73. Find the price of the adult's ticket and the price of a child's ticket.
Accepted Solution
A:
An adult ticket is $20 and a child ticket is $11.
Our system of equations would be:
3A + 4C = 104 2A + 3C = 73
We want the coefficients of one of these variables to be the same in order to eliminate it; we will multiply the top equation by 2 and the bottom equation by 3: 2(3A + 4C = 104) 3(2A + 3C = 73)
6A + 8C = 208 6A + 9C = 219
Subtract the bottom equation:
6A + 8C = 208 -(6A + 9C = 219)
-1C = -11
Divide both sides by -1: -1C/-1 = -11/-1 C = 11
Substitute this into the first equation: 3A + 4(11) = 104 3A + 44 = 104
Subtract 44 from both sides: 3A + 44 - 44 = 104 - 44 3A = 60