Translate the problem into an equation:
The product of two consecutive numbers: x(x+1)
is equal to 35 more than 11 times the sum of the consecutive numbers:
11(x + x + 1) + 35
Set them equal to each other:
x(x+1) = 11(x + x + 1) + 35
x^2 + x = 22x +11 +35
x^2 +x = 22x + 36
x^2 -21x -36 = 0
Factor:
(x-23)(x+2) = 0
Solutions:
x = 23
x = -2
Thus there are two sets of number that works:
23 & 24
and
-2 & -1