The consecutive odd integers have a sum of 36. find the integers

Work Shown:

x = some integer

2x = even integer

2x+1 = odd integer

(2x+1)+2 = 2x+3 = odd integer just after 2x+1

The integers 2x+1 and 2x+3 add to 36

(2x+1)+(2x+3) = 36

2x+2x+1+3 = 36

4x+4 = 36

4x+4-4 = 36-4 ... subtract 4 from both sides

4x = 32

4x/4 = 32/4 divide both sides by 4

x = 8

With x = 8, we can say

2x+1 = 2*8+1 = 17 is the first odd integer

2x+3 = 2*8+3 = 19 is the next odd integer

17+19 = 36, so the answer is confirmed

A non-algebraic way to get the answer is to divide 36 in half to get 18

Then try odd integers around 18, so 19+21 = 40 but thats too high

then maybe try 15+17 = 32, thats too low

17+19 = 36 is right on the money