The sum of three consecutive odd numbers is 111. What is the smallest of the three numbers?

The smallest of the three numbers is ##35##.

Consecutive odd numbers increase (or decrease) by an amount of ##2##. For example, observe ##1##, ##3##, and ##5##. To get from one to the next, add ##2## to the previous number. The problem here is you don't know where to start. In fact, this is your unknown, as you are looking for the smallest of the three numbers. Call this ##x##. Then the next two consecutive odd numbers are ##x+2## and ##x+4##. Add these up, set the sum equal to zero, and solve for ##x##.

##rarrx + (x+2) + (x+4) = 111##

##rarrx + x + 2 + x + 4 = 111##

##rarr3x + 6 = 111##

##rarr3x = 105##

##rarrx=105/3##

##x = 35##