When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23. Find the value of the lesser integer.

Answer 1

Assuming that, x, the lesser integer is odd, then the next consecutive odd integers is x+2.

So, 4(x + 2) - x = 23

3x = 15

x = 5 and x+2 = 7

Answer 2

It is not clear if the original integer n is odd or even. Suppose n is even. Then 4(n+1) -n = 23.

And

4(n+1) -n = 4n+ 4 -n = 23

So

3n + 4 = 23 (subtract 4 from both sides)

3n = 19 (divide both sides by 3)

n = 6 1/3 which is not an integer.

Therefore, n must be odd.

4(n+2) -n = 23

4n +8 -n = 23

3n +8 = 23 (subtract 8 from both sides)

3n = 15 (divide both sides by 3)

n = 5

Check:

4((5)+2) - (5) = 4(7) - 5 = 28 - 5 = 23

and that verifies n=5 as the smaller integer.