Question

The sum of three consecutive odd integers is 18 less than five times the middle number. Find the three integers.

Answer 1

Let us assume the first odd integer to be = x
Then
The consecutive middle odd integer = x + 2
The third consecutive odd integer = x + 4
So we can now write the equation as
x + x + 2 + x + 4 = 5(x + 2) - 18
3x + 6 = 5x + 10 - 18
3x + 6 = 5x - 8
3x - 5x = - 8 - 6
- 2x = - 14
2x = 14
x = 14/2
= 7
So the first odd integer is 7
The second consecutive odd integer = (x + 2)
= (7 + 2)
= 9
The third consecutive odd integer = (x + 4)
= 7 + 4)
= 11
So the three consecutive odd integers are 7, 9, 11.