Question

Find three consecutive odd integers such that the sum of the first and third equals to the sum of the second and 43.

Be sure to show your work and list the integers in this format: (1, 2, 3)

Answer 1

(41, 43, 45)

Explanation:

You want three consecutive odd integers such that the sum of the first and third is 43 more than the second.

Setup

Let n represent the middle (second) of the integers. Then the first is (n-2) and the third is (n+2). The given relation can be written as the equation ...

(n -2) +(n +2) = n +43

Solution

Simplifying gives ...

2n = n +43

n = 43

n-2 = 41

n+2 = 45

The three integers are (41, 43, 45).

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Additional comment

When working consecutive integer problems, it often works well to let a variable represent the middle one, or their average value.