Afurniture shop refinishes chairs. employees use one of two methods to refinish each chair. method i takes 0.5 hours and the material costs $9. method ii takes 2.5 hours, and the material costs $7. next week, they plan to spend 199 hours in labor and $1226 in material for refinishing chairs. how many chairs should they plan to refinish with each method?

method I = 88 chairs

method II = 62 chairs

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