Answer: the price of an adult ticket is $21.5 while the price of a child ticket is $15.5
Step-by-step explanation:
Let x represent the price of an adult ticket.
Let y represent the price of a child ticket.
At an amusement park, the cost of 3 adult tickets and 4 children's tickets is 126.50. This means that
3x + 4y = 126.5 - - - - - - - - - - - 1
Another customer paid 120.50 for 2 adult tickets and 5 children's tickets. This means that
2x + 5y = 120.5 - - - - - - - - - - 2
Multiplying equation 1 by 2 and equation 2 by 3, it becomes
6x + 8y = 253
6x + 15y = 361.5
Subtracting, it becomes
- 7y = - 108.5
y = - 108.5/ -7
y = 15.5
Substituting y = 15.5 into equation 1, it becomes
3x + 4 × 15.5 = 126.5
3x + 62 = 126.5
3x = 126.5 - 62 = 64.5
x = 64.5/3 = 21.5
