You are here:

# Algebra/Finding n

Question
Hi. I need help with a math problem. The problem is 6/(n-4)=10/n and I'm not sure how to solve for n. I've got answers from various sites, but I'm confused because no ine is telling me why I need to do what they are doing so I dont know when to do stuff in the future. Thanks for your help.

Hello Alice,

Whenever two fractions are equal to each other, we can always "cross multiply"
and get an equivalent equation.  Thus, 6/(n-4)=10/n becomes 6n=10(n-4), now
distribute the 10 on the right hand side to get 6n=10n-40.  Then subtract 10n
from both sides (whatever we do on one side of an equation, we must also do on the
other side to preserve the equality)...this gives: -4n=-40.  Now divide both sides by
-4 to get n by itself: n=10 ... thus n=10.

See?

I hope this helps.

A. Mantell

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thank you so much!

Algebra

Volunteer

#### Abe Mantell

##### Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

##### Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook