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February 27, 2015

February 27, 2015

Posted by **can u please help me! please** on Monday, February 18, 2013 at 1:06am.

- algebra!! -
**Reiny**, Monday, February 18, 2013 at 1:55ammultiply both sides by 200ab

200b+200a = ab

200b - ab = -200a

b(200-a) = -200a

b = -200a/(200-a) = 200a/(a-200)

or

a = 200b/(b-200)

let a = 201, then b = 40200

let a = 199 , then b = -39800

let a = 202 , then b = 20200

let a = 198 , then b = -19800

let a = 203 , then b = not an integer !

let a = 197 , then b = not an integer!

let a = 204 , then b = 10200

let a = 205 , then b = 8200

let a = 206 , then b = not an integer, ahhh!

...

let a = 240, then b = 1200

let a = 600 , then b = 240000

let a = 10200 , then b = 204

we have to have (a-200) be divisible into 200a

obviously we cannot use a = 200, but we can go up or down from 200 leaving divisors of ±1 , ±2, ±4, ±5, ±8, ±10, .. as long as that divisor divides evenly into 200a

that is, 200 = 2x2x2x5x5

Wolfram says that there are 69 of these

http://www.wolframalpha.com/input/?i=%28x%2By%29%2F%28xy%29+%3D+1%2F200

- algebra!! -
**Calvin Lin**, Wednesday, February 20, 2013 at 9:23amThis problem has been posted on Brilliant as a current problem in this weeks' Geometry problem set.

I am unable to post an image or internet link to it.

Please refrain from telling the OP the answer.

I ask that moderators take this posting down.

- Calvin Lin

Brilliant Challenge Master

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