OG 216

vinviper1 wrote:If m > 0 and x is m percent of y, then in terms of m, y is what percent of x?

100m
1/100m
1/m
10/m
10000/m

[spoiler]10000/m[/spoiler]

I get the equation but get a bit confused after that. Thanks.

This is a great question for picking numbers. Let's start with the statement "x is m percent of y".

We can say that "10 is 50% of 20".

So, we've picked:

x=10
m=50
y=20

Now, let's try the next statement:

"In terms of 50, 20 is what percent of 10?"

Well, 20 is 200% of 10.

So, we want an answer that gives us 200 when we plug 50 in for m.

100m = 5000
1/100m = fraction
1/m = fraction
10/m = fraction
10000/m = 200

Choose (e).

Might a simple definition help here.

"x is m percent of y means"
x = (m/100)*y ...1

and you have to find "y is what percent of x" you have to find a, where
y = (a/100)*x ...2

solve 1 to get
y = (100*x)/m
now you have to convert this equation to look like 2

y = ( (100*100/m)/100 )*x
and you get a = 100*100/m

1)x is m percent of y.

m * y = x
---
100

Solves to my=100x and y= (100x/m)

2)in terms of m, y is what percent of x.

w=what or the variable you're trying to find

w * x = y
---
100

wx= 100y

3) Plug in y from the 1st equation into the 2nd,

wx=100y
wx=100(100x/m)
wx=(10000x/m)
Multiply both sides by m.

mwx=10,000x
divide by x

mw=10,000
w=10,000/m Ans E.

I'm actually more confused by the explanation OG provided for this problem.

They expressed the first info as: x=y*m/100, which I understand. Then they solved for y: y=x100/m, which I also understand.

But then they multiply the fraction by 100 to "convert to an equivalent percent," thus getting 10000/m. For the life of me, I can't understand why there is need to convert that fraction. Doesn't it already express y as the percent of x? I mean, m/100 is the same as m% so isn't y= x/(m/100) the same as y=x/m *100 and thus already a percent? Why multiply again? Someone please explain this to me.

My personally opinion is that this problem is a bit convoluted. It states that "x is m percent of y..." Technically a percent is a fraction so that m should already be expressed as 0.50, 0.30,.. etc the number doesn't matter. What does is that it is already a fraction of 1. Which means to divide and multiple by 100 is considering the percent of m percent. I know realize the book says the answer is 10,000/m but i would say its wrong and the correct answer should be 1/m.

brianhoppe wrote:Technically a percent is a fraction so that m should already be expressed as 0.50, 0.30,.. etc the number doesn't matter.

Technically, a percent and a fraction are two completely different ways of expressing the same idea - a percent is NOT a fraction.

For example, "50% of 100"is NOT the same as ".5% of 100"; is IS the same as ".5 times 100".