To solve this problem, we can use a system of equations. Let x be the cost of a spicy chicken sandwich and y be the cost of a chicken bite.
From the first order:
14x + 6y = 55.90
From the second order:
7x + 5y = 33.19
We can use elimination method to solve for one of the variables. Multiplying the second equation by 2:
14x + 10y = 66.38
14x + 6y = 55.90
Subtracting the second equation from the first:
4y = 10.48
y = 2.62
Now we can substitute y = 2.62 into either equation to find x:
14x + 6(2.62) = 55.90
14x + 15.72 = 55.90
14x = 40.18
x = 2.87
Therefore, a spicy chicken sandwich costs $2.87 and a chicken bite costs $2.62.