# find three consecutive odd integers such that the sum of the first and the third equals the sum of the second and 13?

### 16 Answers

- TomVLv 71 month ago
If you have 3 consecutive odd integers, the central integer is the mean of the two end integers. Hence the sum of the two end integers is twice the central integer. If the sum is the central integer plus 13, it is obvious the central integer must be 13.

The three integers are 11, 13, 15.

The same argument holds true if the set of integers are consecutive even integers or are any set of integers separated by a constant interval.

Assume the integers are:

n, n+a, n+2a

The sum of the two end integers is n + n+2a = 2n+2a = 2(n+a)

This is obviously double the central integer. The numbers don't even have to be integers. They can be any numbers. The necessary condition is that they be separated by a constant interval.

- Login to reply the answers

- Anonymous1 month ago
Can you pls restate I didn’t really get that

- Login to reply the answers

- Engr. RonaldLv 71 month ago
(2n + 1) + (2n + 5) =2n + 3 + 13

4n + 6 = 2n + 16

4n - 2n = 16 - 6

2n = 10

n = 5 answer//

so

2n + 1 = 2(5) + 1 = 11

2n + 3 = 2(5) + 3 = 13

2n + 5 = 2(5) + 5 = 15

the odd integers are: 11, 13,15 ... answer//

- Login to reply the answers

- sepiaLv 71 month ago
Three consecutive odd integers such that

the sum of the first and the third equals

the sum of the second and 13:

11, 13. and 15

- Login to reply the answers

- How do you think about the answers? You can sign in to vote the answer.
- 1 month ago
1st integer = (x + 1)

2nd integer = (x + 3)

3rd integer = (x + 5)

1st integer + 3rd integer = 2nd integer + 13

(x + 1) + (x + 5) = (x + 3) + 13

2x + 6 = x + 16

2x = x + 10

x = 10

1st integer = 10 + 1 = 11

2nd integer = 10 + 3 = 13

3rd integer = 10 + 5 = 15

hope this helps!

- Login to reply the answers

- ElaineLv 71 month ago
Let the odd integers be n, n +2, n + 4

n + (n + 4) = (n + 2) + 13

2n + 4 = n + 15

2n - n = 15 - 4

n = 11

The integers are 11, 13 15

Verify

11 + 15 = 26

13 + 13 = 26

FYI

n, n +2, n + 4 works for consecutive even integers as well

- Login to reply the answers

- PuzzlingLv 71 month ago
Let n be the first odd integer.

Let n+2 be the second odd integer.

Let n+4 be the third odd integer.

"The sum of the first and the third..."

n + n+4

"...equals the sum of the second and 13"

n + n+4 = n+2 + 13

2n + 4 = n + 15

2n - n = 15 - 4

n = 11

Answer:

11, 13, 15

- Login to reply the answers

- RichardLv 71 month ago
Let the first integer be 2n + 1.

Then, the second integer is 2n + 3.

The third integer is 2n + 5.

So, (2n + 1) + (2n + 5) = (2n + 3) + 13

Adding up each side:

4n + 6 = 2n + 16, or simplify to:

2n + 3 = n + 8

n = 5

so, the first odd number is:

2n + 1 = (2 X 5) + 1 = 11

and the other odd numbers would be 13 and 15

- Login to reply the answers

- DWReadLv 71 month ago
(2n+1) + (2n+5) = (2n+3) + 13

4n + 6 = 2n + 16

n = 5

2n+1 = 11

2n+3 = 13

2n+5 = 15

- Login to reply the answers

- L. E. GantLv 71 month ago
let the integers be

2n + 1, 2n + 3, 2n + 5

then 4n + 6 = 2n + 16

==> 2n = 10

==> n = 5

so

11, 13 and 15

- Login to reply the answers