Question 1152967: A furniture shop refinishes tables. Employees use one of two methods to refinish each table. Method I takes 0.5hours and the material costs$9.Method II takes2 hours, and the material costs$7.Next week, they plan to spend 99 hours in labor and $564 in material for refinishing tables. How many tables should they plan to refinish with each method?
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
Let x be the number of Tables by the Method 1, and
let y be the number of Tables by the Method 2.
Then you have this system of 2 equations in 2 unknowns
0.5x + 2y = 99 (1) (hours)
9x + 7y = 564. (2) (labor cost)
To solve it, Multiply equation (1) by 18 (both sides). Keep equation (2) as is.
9x + 36y = 99*18 (3)
9x + 7y = 564. (4)
Subtract equation (4) from equation (3). You will get
36y - 7y = 99*18 - 564
29y = 1218
y = 1218/29 = 42.
Substitute the found value of y into equation (1) and find x
0.5x + 2*42 = 99,
0.5x = 99 - 2*42 = 15
x = 15/0.5 = 30.
ANSWER. 30 tables by Method 1 and 42 tables by Method 2.
Solved.
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