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If m>0 and x is m percent of y, then, in terms of m,

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If m>0 and x is m percent of y, then, in terms of m, [#permalink]  15 Dec 2008, 14:35
Hello, I am confused by the explaination given for this question. Here it is:

If m>0 and x is m percent of y, then, in terms of m, y is what percent of x?

I understand in the explanation that the equation would be set up initially as x=m/100(y). Then you convert it to y, so that would be 100/m(x)=y.

But then the explanation says that to convert the fraction 100/m to an equivalent percent, multiply by 100. This is the part I do not understand and was hoping for a broader explanation as to why I would do this?
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Re: Percents [#permalink]  15 Dec 2008, 15:31
mdavis wrote:
Hello, I am confused by the explaination given for this question. Here it is:

If m>0 and x is m percent of y, then, in terms of m, y is what percent of x?

I understand in the explanation that the equation would be set up initially as x=m/100(y). Then you convert it to y, so that would be 100/m(x)=y.

But then the explanation says that to convert the fraction 100/m to an equivalent percent, multiply by 100. This is the part I do not understand and was hoping for a broader explanation as to why I would do this?

suppose:
y = 60
m = 15%
x = m% of y/100 = my/100 = (15% of 60)/100 = 9

y = 100x/m

what is y in terms of m(in %)?

(y/x) % = [(100x/m)/x] 100%
(y/x) % = 10,000/m

(y/x)% = (60/9) (100) = 2000/3
10,000/m = 10,000 /15 = 2000/3

therefore (y/x)%=10,000/m
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Re: Percents [#permalink]  15 Dec 2008, 19:37
Thanks for trying to help me out. I guess I am just dense because I get lost halfway through your explanation. Am I reading the problem wrong? I guess I just do not understand why you multiply the other side by 100 to get 10000m/x instead of 100/m. I thought that if you multiply one side of the equation, you need to do that to the other.

I guess to take your example, you said y=60 and m=15. So in the initial equation you get x=15/100(60). The OG would then say you move things so that it would equal 100/15(x)=60. Then it says you would have to change it to a percent (don't understand why because it was a percent on the other side). So it says that it then becomes this 100(100/15)(x)=60. I think what is getting me is multiplying the 100 on the right side without doing anything on the left. Why would I do that? It seems to me that it unbalances the equation.

Sorry to be so dense here. What is it that I am doing wrong?
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Re: Percents [#permalink]  16 Dec 2008, 22:05
mdavis wrote:
Thanks for trying to help me out. I guess I am just dense because I get lost halfway through your explanation. Am I reading the problem wrong? I guess I just do not understand why you multiply the other side by 100 to get 10000m/x instead of 100/m. I thought that if you multiply one side of the equation, you need to do that to the other.

I guess to take your example, you said y=60 and m=15. So in the initial equation you get x=15/100(60). The OG would then say you move things so that it would equal 100/15(x)=60. Then it says you would have to change it to a percent (don't understand why because it was a percent on the other side). So it says that it then becomes this 100(100/15)(x)=60. I think what is getting me is multiplying the 100 on the right side without doing anything on the left. Why would I do that? It seems to me that it unbalances the equation.

Sorry to be so dense here. What is it that I am doing wrong?

lets take another example:

x = 100
y = 50
z = 10

y = (50/100) (100)% = 50% of x
z = (10/50)(100)% = 20% of y

z = (10/100)(100)% = 10% of y
or, z = (y/x) (100)% (z/y)(100)% = (yz/xy) (10,000)% = 10%

So it similar to z as 10,000% of (yz/xy).

what you are doing is taking % of %. so you need to multiply 100% by 100%. so it is 10,000% of .......

Hope you got it.
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Re: Percents [#permalink]  17 Dec 2008, 11:13
mdavis wrote:
Hello, I am confused by the explaination given for this question. Here it is:

If m>0 and x is m percent of y, then, in terms of m, y is what percent of x?

I understand in the explanation that the equation would be set up initially as x=m/100(y). Then you convert it to y, so that would be 100/m(x)=y.

But then the explanation says that to convert the fraction 100/m to an equivalent percent, multiply by 100. This is the part I do not understand and was hoping for a broader explanation as to why I would do this?

"y is what percent of x"
so convert your equation to y/x. This will give you a number that you need to multiply by 100 (%) to get your Percent.
for example if y = 80 and x = 100, y/x gives you 0.8, 0.8 x 100 = 80%

so with your equaion x = (my)/100, converting it to y/x = 100/m
multiply this by 100 to give you percentage being 10000/m
Re: Percents   [#permalink] 17 Dec 2008, 11:13
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