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 5, the three resulting numbers are equal. What is the value of b?
a+6=b−6=5c⟹a=b−12,c=b−65
a+b+c=99⟹b−12+b+b−65=99⟹115b−665=99⟹15b−65=9⟹b−6=45⟹b=51.