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?
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
