Answer:
The five odd numbers are:
23, 25, 27, 29, and 31
Explanation:
A random odd number is written as:
2*n + 1
Where n is an integer.
Then 5 consecutive odd numbers will be:
2*n + 1
2*(n + 1) + 1
2*(n + 2) + 1
2*(n + 3) + 1
2*(n + 4) + 1
Now we want that the sum of the first 3 numbers to be 15 greater than the sum of the two last numbers, then:
(2*n + 1) + (2*(n + 1) + 1) + (2*(n + 2) + 1) = 15 + (2*(n + 3) + 1) + (2*(n + 4) + 1)
Now we just need to solve this for n:
(2*n + 1) + (2*n + 3) + (2*n + 5) = 15 + (2*n + 7) + (2*n + 9)
6*n + 9 = (15 + 7 + 9) + 4*n
6*n - 4*n = 15 + 7 + 9 - 9
2*n = 15 + 7 = 22
n = 22/2 = 11
Then the five numbers are:
(2*11 + 1) = 23
(2*(11 + 1) + 1) = 25
(2*(11 + 2) + 1) = 27
(2*(11 + 3) + 1) = 29
(2*(11 + 4) + 1) = 31