Tanvi is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered 2 child buffets and 2 adult buffets, which cost a total of $92. At another table, the customers ordered 4 child buffets and 2 adult buffets, paying a total of $128. How much does the buffet cost for each child and adult?
Let's call the cost of the child buffet "C" and the cost of the adult buffet "A."
From the problem, we can set up two equations:
2C + 2A = 92 (equation 1)
4C + 2A = 128 (equation 2)
We can solve this system of equations by subtracting equation 2 from equation 1:
(2C + 2A) - (4C + 2A) = 92 - 128
2C - 4C = -36
-2C = -36
C = (-36)/(-2)
C = 18
Plugging the value of C back into equation 1:
2(18) + 2A = 92
36 + 2A = 92
2A = 92 - 36
2A = 56
A = 56/2
A = 28
Therefore, each child buffet costs $18 and each adult buffet costs $28.