Math CentralQuandaries & Queries


Question from George, a student:

Write an equation three consecutive odd numbers whose sum is 75

Hi Gorge,

The three numbers must be odd. It's easy to write an even number since every even number is 2 times some number you can write an even number as $2 \times n$ where $n$ is some number. Every odd number is one more than an even number so you can write any even number as $2 \times n + 1$ where $n$ is some number. Hence you can start a solution this way.

Let the smallest of the three odd numbers be $2 \times n + 1$ where $n$ is some number. The next odd number is 2 more than this number so it's $2 \times n + 1 + 3.$ What is the next odd numbers? Now you have three consecutive odd numbers. Their sum must be 75 so write this as an equation.

Write back if you need more help,

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