SOLUTION: An urban hospital is adding one new nurse practitioner and one new registered nurse to the staff each month. There are five more RNs than LPNs right now, and the product of the tot

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Question 1183642: An urban hospital is adding one new nurse practitioner and one new registered nurse to the staff each month. There are five more RNs than LPNs right now, and the product of the total number of each is three times what it was 5 months ago. How many LPNs are on staff right now?
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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Sorry,  not all the tutors at this forum are familiar with the abbreviations you use in your post.


The rule of a politeness in  Math  (when you come to the scene)  is to speak in understandable  (or commonly accepted)  language.


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My solution is below. 


Let x be the number of LPN.

Then the number of RN is (x+5) now, according to the condition.


The product  of LPN by RN now is x*(x+5).


The product  of LPN by RN 5 months ago was (x-5)*x.


From the description, you have this equation


    x*(x+5) = 3*(x-5)*x


Cancel x in both sides


    x+5 = 3*(x-5)


Simplify and get the answer x= 10.

Solved and explained.