a furniture shop refinshes cabinets. employees use one of two methods to refinish each cabinet. method 1 takes 1 hour and the material costs $6. method 2 takes 1.5 hours and the material costs $4. next week they plan to spend 106 hours in labor and $516 in material for refinishing cabinets. how many cabinets should they plan to refinish with each method?

70 cabinets in method 1 and 24 cabinets in method 2.

Step-by-step explanation:

Let in method 1 they refinish x cabinets and in method 2 they refinish y cabinets.

Now, given that method 1 and method 2 takes 1 hour and 1.5 hours respectively and the material costs for method 1 and method 2 are $6 and $4 respectively.

If they plan to spend 106 hours in labour and $516 in material for refinishing cabinets, then

x + 1.5y = 106 ... (1) and

6x + 4y = 516 ... (2)

Now, solving equations (1) and (2), we get

6 (106 - 1.5y) + 4y = 516

⇒ 5y = 636 - 516

⇒ y = 24 cabinets

From equation (1) x = 106 - 1.5y = 106 - 36 = 70 cabinets. (Answer)