Question

A set of 5 consecutive odd integers adds up to 55. What is the least of the 5 integers?

Answer 1

7

EXPLANATION :

Note that consecutive odd integers differ by 2.

Let x = first odd integer

then the next odd integers will be 2 more than the previous odd integer.

That will be :

x + 2 = second odd integer

x + 4 = third odd integer

x + 6 = fourth odd integer

x + 8 = fifth odd integer

The sum of 5 odd integers is 55

So the equation will be :

`x+(x+2)+(x+4)+(x+6)+(x+8)=55`

Simplify and solve for x :

`\begin{gathered} 5x+20=55 \\ 5x=55-20 \\ 5x=35 \\ x=(35)/(5) \\ x=7 \end{gathered}`

Since x is the smallest odd integer, the answer is 7.