Question 1128991: A furniture company makes large and small chairs. A small chair takes 20 minutes of machine time and 60 minutes of labor to build. A large chair takes 50 minutes of machine time and 90 minutes of labor to build. The company has 69 hours of labor time and 31 hours of machine time available each day. How many of each type of chair is built in a day?
Found 3 solutions by stanbon, ikleyn, MathTherapy:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A furniture company makes large and small chairs. A small chair takes 20 minutes of machine time and 60 minutes of labor to build. A large chair takes 50 minutes of machine time and 90 minutes of labor to build. The company has 69 hours of labor time and 31 hours of machine time available each day. How many of each type of chair is built in a day?
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Labor equality:: 60S + 90L = 69*60 minutes
Machine equality:: 20S + 50L = 31*60 minutes
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Simplify::
6S + 9L = 414
2S + 5L = 186
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Modify and solve for "L"::
6S + 9L = 414
6s + 15L = 558
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Subtract and solve for "L"::
6L = 144
L = 24 (# of Large chairs to build)
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Solve for "S"::
2S + 15L = 558
2S = 558-15*24
S = 279-180
S = 99 (# of Small chairs to build)
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Cheers,
Stan H.
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Answer by ikleyn(52878)  (Show Source):
You can put this solution on YOUR website! .
Let X = # of large chairs and Y = # of small chairs.
The equations are
90*X + 60*Y = 69*60 (1) (minutes of labor time)
50*X + 20*Y = 31*60 (2) (minutes of machine time)
Multiply eq(2) by 3 (both sides). Keep equation (2) as is. You get
90*X + 60*Y = 69*60 (1')
150*X + 60*Y = 3*31*60 (2')
Now subtract eq(1') from eq(2'). You will get
60X = (3*31 - 69)*60
X = 3*31-69 = 24.
Then from eq(2) Y =  = 33.
Answer. 24 large chairs and 33 small chairs.
Solved.
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On the way, I used the Elimination method to solve the system of equations.
So, now you know how it works.
Answer by MathTherapy(10556)  (Show Source):
You can put this solution on YOUR website! A furniture company makes large and small chairs. A small chair takes 20 minutes of machine time and 60 minutes of labor to build. A large chair takes 50 minutes of machine time and 90 minutes of labor to build. The company has 69 hours of labor time and 31 hours of machine time available each day. How many of each type of chair is built in a day?
Let number of small and large be S, and L, respectively
Then we get the following system of equations:
20S + 50L = 31(60)
2S + 5L = 186 ------ Dividing by LCD, 10 ------ eq (i)
60S + 90L = 69(60)
2S + 3L = 138 ------ Dividing by LCD, 30 ------ eq (ii)
2L = 48 ------- Subtracting eq (ii) from eq (i)
Number of large chairs, or 
2S + 5(24) = 186 ------- Substituting 24 for L in eq (i)
2S = 186 - 120
2S = 66
Number of small chairs, or 
STANBON is WRONG!!!
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