# Very easy proportions question

1. Aug 3, 2008

### iamthewalrus

hey its been a while since i had to do proportions so i was wondering if someone could show me how to solve a problem like this: if x increases by a factor of square root of 2, y decreases by 2, how are x and y related. just by looking at it, i can see that y = 1/x^2 but can someone show me a formal solution, i cant seem to come up with one!

ty.

Last edited: Aug 3, 2008
2. Aug 3, 2008

### symbolipoint

Best translation seems to be, directly as:

x*(2^(1/2))=y*(1/2)

But your provided wording may not exactly fit the proportion idea. Anyway, you should transcribe into conventional notation that you can more easily recognize (lack of typesetting here).

3. Aug 3, 2008

### iamthewalrus

hi i tried the approach you suggested but when you solve for y in terms of x using that equation, you get

y = sqrt(2)/x which basically tells me y is inversely proportional to x whereas it is clear y is inversely proportional the square of x...

4. Aug 4, 2008

### symbolipoint

iamthewalrus, possibly I mishandled the original translation. I will rethink this but someone else will probably respond before I do.

5. Aug 4, 2008

### Varnick

IamtheWalrus, if you use Symbolipont's relationship, you should find that

$$y = 2\sqrt{2} x$$

6. Aug 4, 2008

### iamthewalrus

hi Varnick, thanks for your reply and you're right that's what symbolipoint's equation implies but it's not the correct answer. firstly, if y goes down when x goes up, wouldn't that suggest already some type of inverse relationship? the right answer is supposed to be y = 1/x^2 which seems to be more consistent with the conditions I initially stated.

7. Aug 4, 2008

### Varnick

Where have you got this answer from? It does not appear to be consistent with your initial post (your first post would describe a relationship between y and x, not y and x squared).

V

8. Aug 4, 2008

### nothing123

its from an MCAT question that asked about the relationship between intensity and f-stop of a camera. i just replaced the variables with y and x. and it seems plausible that if x increased by the square root of 2, y would decrease by 2 would describe a relationship where y = 1/x^2. that is, if x increases by sqrt(2), y decreases by [sqrt(2)]^2 = 2. anyways, that was the answer and it appears correct but it did not provide a formal proof for it.

9. Aug 5, 2008

### nothing123

sorry posted on a friends account.