Question

A furniture shop refinishes cabinets, Employees use two methods to refinish cabinets. Method I takes 0.5 hours and thematerial costs $10. Method II takes 2.5 hours, and the material costs $4. Next week, they plan to spend 122 hours in labor and$876 in material for refinishing cabinets. How many cabinets should they plan to refinish with each method? (Round to twodecimal places if necessary.)

Answer 1

Let x be the cabinets refinished using the method I and y be the cabinets refinished using method ll.

So:

0.5x +2.5y = 122

10x +4y = 876

Let's solve the system:

Isolating x in the first equation:

0.5x = 122 -2.5y

x= (122 - 2.5y)/0.5

x= 244 - 5y

Now, substituting in the second equation:

10*(244-5y) +4y = 876

2440 -50y+ 4y = 876

-46y = 876-2440

-46y = -1564

y=34

x = 244 -5*34

x= 244 - 170

x = 74

Answer: They should plan to refinish 74 cabinets using method l and 34 using method ll.