Question

If the product of two consecutive integers is decreased by 20 times the greater integer, the result is 442. find the integers

Answer 1

Let the first integer be x.  Then the next consecutive integer is x+1.

Translating the word problem into symbols, x(x+1)-20(x+1) = 442.

Then x^2 + x - 20x - 20 = 442

or      x^2 - 19x - 462 = 0

Solve by completing the square:

          x^2 - 19x + 90.25 - 90.25 - 462 = 0

           (x-9.5)^2 - 552.25 = 0

Taking the positive square root of both sides, we get x-9.5 = 23.5, or
                                                                                    x        = 33

The two consecutive integers are 33 and 34.

Check:  (33)(34)-20(34) = 442 (as expected).