A furniture shop refinishes cabinets. Employees use one of two methods to refinish each cabinet Method I takes 1 hour and the material costs $6. Method II takes 2 hours, and the material costs $5. Next week, they plan to spend 260 hours in labor and $986 in material for refinishing cabinets. How many cabinets should they plan to refinish with each method?

They should refinish 96 tables using method 1

They should refinish 82 tables using method 2

Step-by-step explanation:

Let

a = number of tables refinished using method 1

b = number of tables refinished using method 2

Time equation

a+2b=260 (1)

Cost equation

6a+5b=986 (2)

a+2b=260 (1)

6a+5b=986 (2)

Multiply (1) by 5 and (2) by 2

5a+10b=1,300 (3)

12a+10b=1,972 (4)

Subtract (3) from (4)

7a=672

Divide both sides by 7

a=96

Recall,

a+2b=260

96+2b=260

2b=260-96

2b=164

Divide both sides by 2

b=164/2

=82

They should refinish 96 tables using method 1

They should refinish 82 tables using method 2

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