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(52777)   (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.
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