Answer:
method I = 88 chairs
method II = 62 chairs
Step-by-step explanation:
This problem can be modeled by a system of two linear equations.
Define x as the number of chairs refinished by method I and y by method II
The sum of hours spent on both methods should equal 199 and the sum of total material cost should equal $1226, therefore:


Multiplying the first equation by -18 and adding it to the second equation we can solve for the value of y:

We can now apply the value of y found to the first equation and solve for x:

Therefore, they should refinish 88 chairs with method I and 62 chairs with method II