34 is 51 Percent of J

Date: 11/12/2001 at 18:21:27
From: Michenzie Motl
Subject: Percent problems 

The problem is: 34 is 51% of J.

I haven't really tried to figure it out because I don't know where to 
begin, so that's where I need your help.

Date: 11/14/2001 at 15:39:28
From: Doctor Mike
Subject: Re: Percent problems 
  
Hello Michenzie,
  
I will be glad to tell you how to begin.
  
Back when I was in grade school, my teacher, Mrs. Gill, gave me a very 
useful hint about problems that use the word "of" in them. I mean 
problems that say "half of" or "9/10 of" or "51% of" somewhere in 
them. The hint was that such phrases really are talking about 
multiplication.  
  
For example, a problem that says "half of" would mean the same if you 
replaced that by "1/2 times."  If someone asks you what is half of 24, 
that is the same as asking what is 1/2 times 24. The same thing is
true about replacing "9/10 of" by "9/10 times."
  
But what about 51% of something?  The two examples I just gave used 
fractions like 1/2 and 9/10, but this is a percent. Well, talking 
about percents is a way of talking about PARTS of things, which is
what you are doing with fractions. You have heard of splitting 
something "fifty-fifty" or "50-50," right? That means splitting it 
right down the middle, and giving half to each person. It means this 
because 50 percent is the same as the fraction 50/100, which is the 
same as the fraction 1/2. What you are dealing with in your problem is 
51 percent, which is the same as the fraction 51/100.
  
Now, after ALL this background, your problem
   
      34 is 51% of J  
  
can be re-written as 
  
      34  =  (51/100)*J 
  
So, I have done what I promised, to tell you how to begin. Now, there 
is still some work to do; You have to actually solve for J.  

I wish you good results. Write back to Dr. Math if you have too much 
difficulty.   
  
- Doctor Mike, The Math Forum
  http://mathforum.org/dr.math/