jen butler has been pricing speed train fares for a group trip to new york. three adults and four children must pay $94. two adults and three children must pay $66. find the price of the adults ticket and the price of a child’s ticket
Let's assume the price of an adult's ticket is x and the price of a child's ticket is y.
From the given information, we can form two equations:
3x + 4y = 94 ...(1)
2x + 3y = 66 ...(2)
Multiplying equation (2) by 2, we get:
4x + 6y = 132 ...(3)
Now, we can solve equations (1) and (3) simultaneously.
Subtracting equation (1) from equation (3), we get:
4x + 6y - (3x + 4y) = 132 - 94
x + 2y = 38 ...(4)
Now, we can solve equations (4) and (2) simultaneously by using the elimination method.
Multiplying equation (4) by 3, we get:
3(x + 2y) = 3(38)
3x + 6y = 114 ...(5)
Subtracting equation (5) from equation (2), we get:
(2x + 3y) - (3x + 6y) = 66 - 114
2x + 3y - 3x - 6y = -48
- y = -48
y = 48
We substitute y = 48 in equation (4) to find the value of x:
x + 2(48) = 38
x + 96 = 38
x = 38 - 96
x = -58
Since the price of a ticket cannot be negative, we conclude that there is an error in the given information or calculation process. Please check the given information again or provide more details to solve correctly.