The product of two consecutive integers is 482 more than the next integer. What is the largest of the three integers?

Question

Genesis Allen · Accepted Answer

The largest is 24 or -20.
Both solutions are valid.

Let the three numbers be #x, x+1 and x+2# The product of the first two differs from the third by 482. #x xx (x+1) - (x+2) = 482# #x^2+x -x -2 = 482# #x^2 = 484# #x = +-sqrt484# #x = +-22# Check: #22 xx 23 - 24 = 482# #-22 xx -21 - (-20) = 482# Both solutions are valid.

Eva Abramson · Answer

undefined Let the consecutive integers be x and x + 1.

According to the given information, the product of these two consecutive integers is 482 more than the next integer, which can be expressed as:

x(x + 1) = (x + 2) + 482

Expanding and simplifying the equation, we get:

x^2 + x = x + 484

Bringing all terms to one side, we have:

x^2 + x - x - 484 = 0

This simplifies to:

x^2 - 484 = 0

Now, we can solve this quadratic equation to find the value of x. The solutions are x = 22 and x = -22. Since we're looking for the largest of the three integers, the largest integer is x + 2 when x = 22, which equals 24. Therefore, the largest integer is 24.