The product of two consequtive postivite integers us equal to eleven times the sum of thw two integers plus 35. find the integers

We can represent the consecutive numbers with x and x+1.
Next, we can translate the sentences into an equation, factor, and solve for x.

x(x+1) = 11(x + x + 1 + 35)
x^2 + x = 11(2x + 36)
x^2 + x = 22x + 396
x^2 - 21x - 396 = 0
(x + 12)(x - 33) = 0
Since the question is asking for a positive no. we know the first integer must be 33. The next integer would be 34 because it is 1 more than 33.