The system of equations that models this situation is:
6l + b = 55.90
7s + 5b = 33.19
where l represents the cost of a spicy chicken sandwich, s represents the cost of a regular chicken sandwich, and b represents the cost of an order of chicken bites.
To solve for the cost of each item, we can use elimination method to eliminate the variable b. Multiplying the first equation by 5 and the second equation by -1, we get:
30l + 5b = 279.50
-7s - 5b = -33.19
Adding the two equations together, we get:
30l - 7s = 246.31
Next, we can use either equation to solve for one of the variables. For example, we can use the first equation to solve for b:
6l + b = 55.90
b = 55.90 - 6l
Substituting this expression for b into the second equation, we get:
7s + 5(55.90 - 6l) = 33.19
7s - 30l = -223.81
Now we have two equations:
30l - 7s = 246.31
7s - 30l = -223.81
We can solve this system of equations using elimination method again. Multiplying the second equation by 4 and adding itto the first equation, we get:
30l - 28l = 21.5
2l = 21.5
l = 10.75
So the cost of a spicy chicken sandwich is $10.75.
Substituting this value of l into the equation 6l + b = 55.90, we get:
6(10.75) + b = 55.90
b = 55.90 - 64.50
b = -8.60
Since the cost of an order of chicken bites cannot be negative, we made an error in our calculations. We can check our work by substituting the values of l and b into the second equation:
7s + 5b = 33.19
7s + 5(-8.60) = 33.19
7s - 43 = 33.19
7s = 76.19
s = 10.88
So the cost of a regular chicken sandwich is $10.88.
Therefore, the exact cost of each item is:
- Spicy chicken sandwich: $10.75
- Regular chicken sandwich: $10.88
- Chicken bites: $8.60 (rounded to the nearest cent)