You can represent an odd integer with the expression 2n+1, where "n" is any integer. What are three consecutive odd integers that have a sum of 63.

Question

Write and solve an equation to find out the three consecutive odd integers that have a sum of 63.

Answer 1

As consecutive odd numbers differ by two (example: 3, 5, 7), the first odd number can be expressed as 2n + 1, the next can be found by adding two to the first to get 2n + 1 + 2 which simplifies to 2n + 3. Finally the expression for the third consecutive odd integer can be found by adding two to the previous, 2n + 3, to get 2n + 5.  Adding these three together and setting them equal to your sum gets the equation

 

2n + 1 + 2n + 3 + 2n + 5 = 63

 

Combine like terms and solve For n.

Once you have n, you must substitute it back into your three expressions (2n + 1, 2n + 3, 2n + 5) to find the three odd integers. 

 

Hope this helps :)

Answer 2

Let's let 2n+1 be the middle odd integer...

Then our integers are 2n-1, 2n+1, 2n+3

 

2n-1 + 2n + 1 + 2n + 3 = 63

 

6n + 3 = 63

 

6n + 60

 

n = 10

 

2n-1 = 19

2n+1 = 21

2n+3 = 23