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The sum of three numbers a, b, and c is 99. If we increase a by 6, decrease b by 6 and multiply c by \(4\), the three resulting numbers are equal. What is the value of b?

 Apr 30, 2022
 #1
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a  + b +  c =  99

 

a + 6  = b - 6                   4c = b - 6

a =  b -12                          c = (b  - 6)  / 4

 

This implies that

 

(b -12)  +  b +  (b -6) / 4 = 99   

 

2b - 12  +  (b - 6) /4 =  99      multiply through by 4

 

8b -48 + b - 6  =  396

 

9b  =  396  + 54

 

9b  = 450

 

b=  450 / 9  =   50

 

a = 38  b  = 50  c =  11

 

 

cool cool cool

 Apr 30, 2022

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