Question 133737: am trying to figure out a problem, that I cannot, for the life of me seem to answer by showing my work. The answer is supposed to be either -1&-2 or 3&4.
Here is my question.
The sum of two consecutive integers is 5 less than their product. Find the integers.
I found them, but I cannot show HOW I got them. ??
Answer by dolly(163)   (Show Source):
You can put this solution on YOUR website! Hi,
I'll help you out.
Let the consecutive integers be x, x+1.
Then by the given data,
x(x+1) = x + x+1 + 5
==> x^2 + x = 2x + 6
==> x^2 + x - 2x - 6 = 0
==> x^2 - x - 6 = 0
==> x^2 - 3x + 2x - 6 = 0
==> x(x - 3) + 2(x - 3) = 0
==> (x - 3) (x + 2) = 0
==> x - 3 = 0 or x + 2 = 0
==> x = 3 or x = -2
If x = 3, then other number is 4 [as (x+1)]
So the integers are 3 and 4.
If x = -2, then the other number is = -1 [ as x+1]
So the integers are -2 and -1.
Hope this helps.
good luck!!!
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