Answer: adult ticket cost $51.5
Children's ticket cost $1.125
Explanation:
Let x represent the cost of one adult ticket.
Let y represent the cost of one children's ticket.
Three adults and four children must pay $159. This means that
3x + 4y = 159 - - - - - - -1
Two adults and three children must pay $112. This means that
2x + 3y = 112 - - - - - - - 2
Multiplying equation 1 by 2 and equation 2 by 3, it becomes
6x + 8y = 318 - - - - - - - -3
6x + 24y = 336 - - - - - - -4
Subtracting equation 4 from equation 3, it becomes
-16y = -18
y = -18/-16 = 1.125
Substituting y = 1.125 into equation 1, it becomes
3x + 4×1.125 = 159
3x + 4.5 = 159
3x = 159 - 4.5 = 154.5
x = 154.5/3 = 51.5