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Simple Arithmetic Question

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Simple Arithmetic Question [#permalink] New post 16 Nov 2013, 09:18
Hello all, I have a question regarding arithmetic, which seems simple enough but when I come across this step in a problem I cannot say that I recognize the need for it. I will give you an example.

Solve the following for d:

y(t-d/x)=d/2

2xy(t-d/2x)=dx*

2xyt-dy=dx
2xyt=dx+dy
2xyt=d(x+y)
(2xyt)/(x+y)=d

The boldface equation represents my problem, namely the step when one multiplies both sides by dx, specifically the variable x. I am having trouble with the logic of doing this and have come to the conclusion that this is done in order to cancel out the x in (d/2x). Is this correct?

Thanks in advance!
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Re: Simple Arithmetic Question [#permalink] New post 17 Nov 2013, 12:15
Expert's post
If I am reading this equation correctly, then this is how you would approach it:

y(t-d)/x=d/2

Multiply both sides by 2, in order to get 2y(t-d)/x=d
Multiply both sides by x, in order to get 2y(t-d)=dx
Distribute, in order to get 2yt-2yd=dx
Move the term with d to right, to get 2yt=dx+2yd
Factor out the d, to get 2yt=d(x+2y)
Divide by x+2y, to isolate d and get d=2yt/(x+2y)

If you struggle with the multipying by the denominator portion, I would recommend doing them one at a time. So rather than multiplying through by 2x, multiply by 2 first, and then x in the next step.

I hope this helps!!!
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Re: Simple Arithmetic Question   [#permalink] 17 Nov 2013, 12:15
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