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.

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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