Expert: Steve Holleran - 8/7/2008

Question
Hello-

Can you help me with the following algebra equation?  And any explanation would be appreciated.

Thanks, Mac

I am thinking of three consecutive negative numbers. If I multiply the first with the second and then subtract three times the third, the result is 57. What are the numbers?  

Answer
Hi Mac,

Usually when you deal with consecutive integer problems, people like to name the integers x, x+1 and x+2, since they differ by one.  But I like to name them slightly differently,

First = x - 1            Second = x              Third = x + 1

(Actually, it really doesn't matter all that much, its just sometimes easier to use the names I use)

Okay, so then here we have the equation

                 (x - 1)*x -3(x + 1) = 57

So,                x^2 - x -3x - 3 = 57

or                 x^2 - 4x - 60 = 0

Now factor this:   (x - 10)(x + 6) = 0 so x = 10 or -6.

since you want negative numbers, then x = -6, so the three consecutive numbers are

                        -7, -6, -5

Check:  -7 * -6 -3(-5) = 42 + 15 = 57.

Hope this helps
Steve