(100 - y) / (100) = (100) / (100 + x)

Cross-multiply 100,

100 - y = (10,000 / (100 + x))

100 - (10,000 / (100+x)) = y

I hope that this is what you are expecting.

I see the solution when you multiply both sides by 100 but I don't understand why you can't cross multiply and get the same equation.

In other words:

(100 - y) / (100) = (100) / (100 + x)

--->(100-y) (100 + x) = (100) (100)

if you cross multiply as mentioned above, you will not get the solution mentioned in the original post.

Why?

pkw209 wrote:I see the solution when you multiply both sides by 100 but I don't understand why you can't cross multiply and get the same equation.

In other words:

(100 - y) / (100) = (100) / (100 + x)

--->(100-y) (100 + x) = (100) (100)

if you cross multiply as mentioned above, you will not get the solution mentioned in the original post.

Why?

100 - (10,000 / (100+x)) = y this is nothing but y=100x/(100+x) the exp which u are getting after cross multiplication


(100 - y) / (100) = (100) / (100 + x)

--->(100-y) (100 + x) = (100) (100)

=10^4+100(x-y)-xy=10^4
or 100x-y(100+x)=0
or y=100x/(100+x)

its the same

will explain it to you step by step:-

1)[(100-y)/100] = [(100)/(100 + x)]
2)Since we want the value of y, we keep it in the L.H.S. numerator and x on the RHS and transpose 100.
3)(100-y) = [(100 x 100)/(100 + x)]
4)-y = [(100 x 100)/(100 + x)] -[100]
5)Multiplying by -1 on both sides to get positive value of y, we get
6)y = 100 - [(100 x 100)/(100 + x)]

I hope the explanation is clear now.

pkw209 wrote:Sub-portion of a Manhattan GMAT Question:

(100 - y) / (100) = (100) / (100 + x)

What is y in terms of x?

Apparently, the answer is [spoiler](100) - ((10,000) / (100 + x )) [/spoiler]

Can someone please explain?

I tried cross-multiplying but I get a different answer.

I can get the answer if I multiple both sides by 100 but why can't I cross-multiply and get the same solution?

Thanks.

Its simple though ...
(100 - y) / (100) = (100) / (100 + x)
multiply 100 both sides , u will get
100-y = 100x100/(100 + x)
add y both side u will get
100 = [100x100/(100 + x) ] + y
--> 100 = 10000/(100 + x) ] + y
subtract [10000/(100 + x) ] both sides
100 - [10000/(100 + x) ] = y
--> y= 100 - [10000/(100 + x) ] = (100) - ((10,000) / (100 + x )) (isn't both looking similar rather equal )

I tried to solve by simple steps ....just like layman ....hope u get it....

Guys-

Appreciate the help but none of you are answering my original question.

I can figure this out by multiplying both sides by 100.

However, I cannot seem to do so when I cross multiply.

This is my step by step process after cross-multiplying:

(100-y) (100 + x) = (100) (100)

10000 + 100x - 100y - xy = 10000

100x = 100y + xy

100x = y(100 + x)

100x / 100 + x = y

THIS IS NOT THE ANSWER. What am I doing wrong?

ANSWER = (100) - ((10,000) / (100 + x ))

100-y/100 = 100/100+x

dont cross multiply yet, instead multiply the RHS with denominator of the first fraction

(100-y) = 100 * (100/(100+x))

(100-y) = ((100*100)/(100+x))

(100-y) = ((100)^2)/(100+x))

[100- ((100)^2)]/(100+x))] = y

Hope this helps.

Thanks, but why can't I cross-multiply in that first step?

It's always natural for me to cross-multiply so I'm just trying to figure out why I can't.

100- 10000/(x+100) = 100x/100+x
if u do like u did u ll have to

100x + 10000 - 10000 / 100 + x add 10000 and minus 10000 so it stays the same
= 100 (x+100) / (x+100) - 10000 /(x+100)= 100 -10000 / (x+100)

i agree it s not evident to do but that s the trick...they know that u re gonna get stuck there so u better consider to try the second option
hope this helps