The miller family visited mama's kitchen and ordered 4 hamburgers and 3 medium fries and paid $18.69. james ordered a medium drink, a hamburger, and 2 medium fries and paid $8.66. steven ordered 2 hamburgers, medium fries, and a medium drink for $10.27. how much did each item cost?

To answer the question, let x be the cost of each hamburger, y be the cost of each medium fries, and z be the cost of each medium drink. The equations that are described in the problem are,
       (Miller )        4x + 3y = 18.69
       (James)       x + 2y + z = 8.66
       (Steven)      2x + y + z = 10.27
Solving simultaneously for the values of the variables give x = 3.36, y = 1.75, and z = 1.8. 
Thus, each hamburger costs $3.36. Each medium fries cost $1.75, and each drink costs $1.8.