SOLUTION: A furniture shop refinishes chairs. Employees use 2 methods to refinish the chairs. Method 1 takes 0.5 hours and the material cost 10$. Method 2 takes 2.0 hours, and the material c

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: A furniture shop refinishes chairs. Employees use 2 methods to refinish the chairs. Method 1 takes 0.5 hours and the material cost 10$. Method 2 takes 2.0 hours, and the material c      Log On


   



Question 1198674: A furniture shop refinishes chairs. Employees use 2 methods to refinish the chairs. Method 1 takes 0.5 hours and the material cost 10$. Method 2 takes 2.0 hours, and the material costs 7$. Next week, they plan to spend 98 hours in labor and 508$ in material for refinishing chairs. How many chairs should they plan to refinish with each method?(round to two decimal places if necessary)
Answer by ikleyn(52778) About Me  (Show Source):
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A furniture shop refinishes chairs. Employees use 2 methods to refinish the chairs.
Method 1 takes 0.5 hours and the material cost 10$.
Method 2 takes 2.0 hours, and the material costs 7$.
Next week, they plan to spend 98 hours in labor and 508$ in material for refinishing chairs.
How many chairs should they plan to refinish with each method?
(round to two decimal places if necessary)
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        The rounding instruction is absurdist,  since the answer must be in integer numbers.


Let x be the number of chairs by Method 1;
    y be the number of chairs by Method 2.


Write equations as you read the problem

    0.5x + 2y = 98    (hours of labor)    (1)

     10x + 7y = 508    (dollars)          (2)


To solve, multiply equation (1) by 20; then subtract equation (2) from it.

You will get simple equation for single unknown y

           20*2y - 7y = 20*98 - 508

or

                33y   =    1452

                  y   =    1452/33 = 44.


Having y= 44, find x from equation (2)

    10x + 7*44 = 508

    10x = 508 - 7*44 = 200

      x              = 200/10 = 20.


ANSWER.  10 chairs by Method 1 and 44 chairs by Method 2.

Solved.