Expert: Lynn Houston - 8/22/2008

Question
QUESTION: 5/2 * N = 98 - N

ANSWER:    
5/2 * N = 98 - N  add n to both sides
5n/2 + n = 98  multiply everything by 2 to get rid of the fraction
5n + 2n = 196  add like terms
7n = 196  divide by 7
n = 28

Let me know if anything's not clear..

---------- FOLLOW-UP ----------

QUESTION: WHERE DID THE ADDITION COME IN AT WITH 5N + 2N IF THE PROBLEM WAS
5/2 (MULTIPLIED BY) N = 98 - N ?

Answer
I explained what I did at each step (after the eq)

5/2 * n is the same as 5/2 * n/1, which equals 5n/2.  In order to get all the n's on one side of the = sign, you have to add n to both sides.  That gives you
5n/2 + n = 98

To get rid of the fraction, multiply everything by 2.

(5n/2)*2 + 2*n = 98*2 or
5n + 2n = 196 (the 2's in the fraction cancel out leaving 5n)

add the n's and you get
7n = 196

dividing by 7 yields
n = 28

Now, I suppose the original problem might be
5/2n = 98-n

If that's the case, you would still handle it the same way, but to start, you'd multiply everything by 2n to get
5 = 196n - 2n^2  rearranging the terms gives you
2n^2 - 196n + 5 = 0  Now you'd have to use the quadratic formula, so depending on what grade you're in, I'm thinking it's probably the first way I solved it that was right.