Question

The number of people in Blue Moon and the number of people in Bored Stiff are consecutive odd integers that add together to be 3644. Of their are more people in Blue Moon than Bored Stiff. How many people are in each city.

Answer 1

Answer: The number of people in Blue Moon and the number of people in Bored Stiff are consecutive odd integers that add together to be 3644

Explanation:

Answer 2

1823 people in Blue Moon

1821 people in Bored Stiff

Explanation:

Any odd integer can be written as:

2n+1

where n is any integer (even or odd), for example with

n=0 -> 1,

n=1 -> 3,

n=2 -> 5

...

now, the problem states that we have two consecutive odd numbers whose add to 3644, that is:

(2n+1) + (2(n+1) + 1) = 3644

2n + 1 + 2n + 2 + 1 = 3644

4n + 4 = 3644

4n = 3644 - 4

4n = 3640

n = (3640/4) = 910

Therefore, since there are more people in Blue Moon than in Bored Stiff, there are:

2*911 + 1 = 1823 people in Blue Moon

2*910 + 1 = 1821 people in Bored Stiff

** 1823 + 1821 = 3644 (total number of people)