anonymous
  • anonymous
Fool's problem of the day, How many ordered pair of \((x,y)\) are there such that \(x, y \in \mathbb{Z} \) and \( \frac 2 x - \frac 3 y = \frac 1 4 \) Good luck!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ParthKohli
  • ParthKohli
Oops, maybe this involves some trial and error :P
ParthKohli
  • ParthKohli
What is \(\mathbb{Z}\) in here?
anonymous
  • anonymous
http://en.wikipedia.org/wiki/Integer

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More answers

ParthKohli
  • ParthKohli
This works with -8 and -6
ParthKohli
  • ParthKohli
If b is -8 then a will be -16
ParthKohli
  • ParthKohli
I see a lot of solutions to this :/
anonymous
  • anonymous
Not many, less than 25 I believe ;)
ParthKohli
  • ParthKohli
24 or 23 or 22.. I guess
ParthKohli
  • ParthKohli
The minimum of b is I guess -36 maximum is 84
anonymous
  • anonymous
Don't guess, try to form a analytic approach :)
ParthKohli
  • ParthKohli
Oh wait, it goes further.
ParthKohli
  • ParthKohli
Your problem is hard.
anonymous
  • anonymous
No spoiler please :)
ParthKohli
  • ParthKohli
How do we do it by the way?
anonymous
  • anonymous
It's problem of the day, it's supposed to be interesting. However my approach takes less than 10 seconds ;) I will post it later though.
anonymous
  • anonymous
is the answer 5? @FoolForMath ?
ParthKohli
  • ParthKohli
No Arnab.
anonymous
  • anonymous
okay, we can get after simplification.. x=8y/(y+12) as x is an integer, 8y must be a multiple of y+12 8y=2*2*2*y so, here are possible equations y+12=1 y+12=2 y+12=4 y+12=8 y+12=2y y+12=4y y+12=8y as y +12 is a factor of 8y all the equations except the last one will satisfy for an integral value of y so, the answer is.. 6 ordered pairs
anonymous
  • anonymous
not 5^^
anonymous
  • anonymous
sorry, there will be other options too if RHS is negative y+12=-1 y+12=-2 ................. and so on.. for y to be an integer, there are another 5 solutions so, total 11
anonymous
  • anonymous
8?
anonymous
  • anonymous
is it right?
ParthKohli
  • ParthKohli
No, not right
anonymous
  • anonymous
the equation is equivalent to (x-8)*(y+12)=-96 so the answer is 11
ParthKohli
  • ParthKohli
Na na
anonymous
  • anonymous
is all the way wrong or just the 11?
anonymous
  • anonymous
22
anonymous
  • anonymous
I m pretty sur it's 22
anonymous
  • anonymous
24
anonymous
  • anonymous
is 24 correct answer.?
ParthKohli
  • ParthKohli
No, you are close by the way
anonymous
  • anonymous
I was able to find 11 ordered pairs that are solutions: (7, 84) (6,36) (5,20) (4,12) (2,4) (-4,-4) (-8,-6) (-16,-8) (-24,-9) (-40,-10) (-88,-11) I think there might be more, but im missing an idea.
anonymous
  • anonymous
HINT: There are 23 of them.
anonymous
  • anonymous
Real challenge is to find a quick analytic approach :)
anonymous
  • anonymous
yeah i just found the other 12, making 23.
anonymous
  • anonymous
Most people probably got that:\[8y-12x-xy = 0\]There is a way you can factor this to get an idea of how many solutions there are...
anonymous
  • anonymous
That's right joe! Congrats man!
anonymous
  • anonymous
ty :)

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