Question

Two people have offices that are consecutive odd numbers with a sum of 14,812. What are the office numbers of these two people

Answer 1

In general, an odd number is given by the expression:

`2n-1,n=1,2,3,\ldots`

Then, let's say that the larger number of the two is 2m-1, the second number has to be then (2m-1)-2 because they are consecutive odd numbers.

We can add those two numbers and solve for m, as follows:

`\begin{gathered} (2m-1)+((2m-1)-2)=14812 \\ \Rightarrow2m-1+2m-3=14812 \\ \Rightarrow4m=14812+4=14816 \\ \Rightarrow m=(14816)/(4)=3704 \end{gathered}`

Therefore, the two numbers are:

`\begin{gathered} 2m-1=2\cdot3704-1=7407 \\ 2m-3=7405 \\ 7407+7405=14812 \end{gathered}`

The answer is 7405 and 7407