Answer:
The adult's ticket cost $15 and the child's ticket cost $13
Step-by-step explanation:
System of Equations
Let's call:
x = price of the adult's ticket
y = price of the child's ticket
Three adults and four children must pay $97, thus:
3x + 4y = 97 [1]
Two adults and three children must pay $69, thus:
2x + 3y = 69 [2]
Multiplying [1] by -2 and [2] by 3:
-6x - 8y = -194 [3]
6x + 9y = 207 [4]
Adding [3] and [4] (the x's cancel out):
-8y + 9y = 13
y = 13
From [1]
3x + 4*13 = 97
3x + 52 = 97
Subtracting 52:
3x = 45
Dividing by 3:
x = 15
The adult's ticket cost $15 and the child's ticket cost $13
