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26 July, 06:02

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?

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  1. 26 July, 06:20
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    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)
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