PLEASE HELP!!! IT'S 3 AM HERE AND I NEED THIS HOMEWORK EXPLAINED!!!
OpenStudy user s.k has 343 fans less than a64. If s.k gets 3 fans a week while a64 gets 2 fans a week, how long will it take s.k to get twice the fans a64 has?

- lgbasallote

- chestercat

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- saifoo.khan

LOL. nice thought.

- saifoo.khan

s.k. fans = x
a64 fans = y
y = 343 + x
i get till here..

- lgbasallote

im thinking y + 2a = x + 3a?

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## More answers

- Akshay_Budhkar

After z weeks the number of fans of s.k= x+3z and a64= y+2z

- lgbasallote

no wait..that's for them to equal..

- lgbasallote

if s.k. will double then
2(y + 2z) = x + 3z?

- Akshay_Budhkar

now we want them to be twice,
so we want
x+3z=2(y+2z)

- ganeshie8

y1 = 3/7 x
y2 = 2/7 x + 343

- lgbasallote

x + 3z = 2y + 4z
x - 2y = z
what does that mean?

- lgbasallote

x - 2(343 + x)?

- ganeshie8

y1 = 3/7 x
y2 = 2/7 x + 343
y1 = 2y2
solve for x

- lgbasallote

how did you get those @ganeshie8 ?

- ganeshie8

y1: number of fans of sk
y2 : number of fans of a64
y1 is increasing his fans at a rate of 3 per 7 days right
so slope of y1 is 3/7
put y1 equation in slope intercept form

- Akshay_Budhkar

yea agreed^ why did i introduce a new variable O_O?

- saifoo.khan

lol ^

- ganeshie8

to start with, a64 has 343 as y intercept..
hope you get the idea..

- lgbasallote

3/7 x = 2(2/7x +343)
3/7 x - 4/7 x = 868
-1/7 x = 868???
this seems weird

- lgbasallote

uhm it's 686 lol

- lgbasallote

but still negative so weird o.O

- saifoo.khan

So sk should start asking people to unfan him? :O

- lgbasallote

lol =)))))

- saifoo.khan

Sounds like a plan. NOT.

- lgbasallote

s.k should put up a teenage asian girl...

- lgbasallote

pic

- saifoo.khan

Ok, this sounds like a better plan. :D

- saifoo.khan

what is this guy typing from a hour?

- lgbasallote

even with values im getting negative lol

- ganeshie8

me.. ? im not typing anythign... just watching hindi movie
i thoutht lgba got the answer... ?

- saifoo.khan

No, i was talking about lgba.

- lgbasallote

no i didnt get the answer..im getting negatives

- lgbasallote

the time when they equal is just easy...could it be that it's impossible for s.k to get double the fans of a64?? o.O

- saifoo.khan

Possibility..

- ganeshie8

yeah that can happen in reality... but equations.. we should get +ve numb er of days

- lgbasallote

let's try solving for equal first...
x + 3z = y + 2z
z = y - x <---this is the time when they become equal

- lgbasallote

assuming they are already equal
let a be their values
a + 3n = 2(a + 2n)
a + 3n = 2a + 4n
a - 2a = n <---the time when they double

- lgbasallote

so if z + n = -a + a = 0??? o.O

- saifoo.khan

LOL.

- Akshay_Budhkar

equal? u want it twice..

- lgbasallote

wth am i doing wrong =_=

- lgbasallote

well it didnt work lol..i just tried

- lgbasallote

why am i getting negative @Akshay_Budhkar ? any ideas>

- Akshay_Budhkar

i am working on it gimme a moment

- lgbasallote

ugh i gtg...will be back in an hour...
if any one of you got some ideas pls feel free to post it here

- ganeshie8

ok me too confused..

- lgbasallote

i dont think i did anything wrong in the solution :/

- Akshay_Budhkar

are we missing an equation??

- Akshay_Budhkar

yea we need another equation, the answer will depend on the initial values of a and b!! try taking two diff sets of the numbers and solving

- Akshay_Budhkar

@saifoo.khan ^

- anonymous

I don't think you can solve this until you have another equation.
We have 3 variables (a= s.k fans, b=a64 fans, and w=weeks) but only two equations, so it is unsolvable. right?

- lgbasallote

well x and y dont really matter. as long as you get a numerical value...but let's say s.k has 914 fans and a64 was 1257..it still becomes negative

- lgbasallote

@ganeshie8 still nothing? even if there are values?

- ganeshie8

343 + 3t = 2{ 2t}
=> t = 343 weeks
in 343 weeks sk fans will become twice that of a64.
i am still lost in straight lines.. i want to see you or someone else explain the answer @lgbasallote @shubhamsrg @abstracted @Akshay_Budhkar

- ganeshie8

@mathslover

- lgbasallote

how did you get 343 again?

- blockcolder

You can just say that every week, s.k's lead will be reduced by one so that after 343 weeks, s.k's lead will be zero.

- lgbasallote

wait what?

- Akshay_Budhkar

@ganeshie8 the straight line stuff wont work, the intercept is wrong, you dont know the intercept.
@lgba the question is incomplete...

- saifoo.khan

@lgbasallote , come up with the complete question next time! -_-
i want to find a way out.

- ganeshie8

@Akshay_Budhkar ,straight line logic may not tell the answer straight away.. but it works.
@saifoo.khan , the question @lgbasallote posted is complete.
answer is :
sk can never achieve his goal. because with a 3t rate he can never reach 2(2t) value !!
3t < 2 (2t + 343)
3t < 4t + ....

- Akshay_Budhkar

@ganeshie8 it is pretty illogical... he can achieve his goal!! He is going at a faster rate man

- Akshay_Budhkar

lol take real life example of 0 fans and 343 fans and solve, it works

- ganeshie8

for positive values of t,
3t <= 2(2t + 300 )
u agree... ?

- ganeshie8

@Akshay_Budhkar

- lgbasallote

but how could it not be possible?? o.O i mean soon s.k is gonna overtake a64 then after that s.k will always be leading there should be a time when s.k will get twice :O

- lgbasallote

let's say both of them start at 0...
1st week - s.k is 3... a64 is 2
2nd week - 6 - 4
3rd week - 9 - 6
4th week - 12 - 8
5th week - 15 - 10
6th week - 18 -12
see how s.k's lead is gettingbigger...that should double sometime

- anonymous

Let \(x\) be a64's number of fans. Let \(y\) be s.k.'s number of fans. We have
\(y(x; w=0)=x_i-343.\)
which is the initial value for \(y\) based on the initial value of \(x.\) Based on how they gain fans, we have:
\(y(x,w)=x_i-343+3w.\)
We want to find the point at which \(y(x,w)=2x(w)\). Note that \(x(w)=x_i+2w.\) Thus we have,
\(x_i-343+3w=2x_i+4w.\)
Let's let \(x_i\) be a constant. So, we have:
\(-x_i-343=w\)
We assume that \(x_i \in \mathbb{Z}^+.\)
This tells us that \(y(x,w)\) will never have twice as many fans as \(x(w)\) if the functions behave as they have been defined. It actually says that we would have to go "backward" to reach a point where \(y(x,w)\) had twice as many fans as \(x(w)\).
Also, you contradicted yourself, lgba:
"let's say both of them start at 0..."
This contradicts the premise that they would start in relation to one another. (i.e. \(y(x;w=0)=x_i-343\) and \(x(w)=x_i+2w.\))
Now let's suppose this: Both \(x\) and \(y\) start at some value \(x_0\) and \(y_0\) respectively. Their growth functions are \(x(w)=x_0+2w\) and \(y(w)=y_0+3w.\) If we want to find the point at which \(y(w)=2x(w),\) we have \(y_0+3w=2x_0+4w\) which is \(w=y_0-2x_0.\) You can see how this makes no sense in your original presumptions.
We can continue this logic further and deduce that this problem makes no sense if \(x_0 > \frac{y_0}{2}.\)
What I find most interesting is that while there is no point in future time that \(y(w)=2x(w),\) there is a point where \(y(w)=x(w).\) This happens to be \(w=x_0-y_0.\) It is this fact that makes one speculate that there is a point where \(y(w)=2x(w)\), but there is no such point in future time.

- anonymous

Oh, cool! I also figured out something else:
\[
\begin{align}
f(x)&=m_fx+b_f\\
g(x)&=m_gx+b_g\\
\lim_{x \to \infty }\frac{f(x)}{g(x)}&=\frac{m_f}{m_g}
\end{align}
\]
This explains everything.

- anonymous

(Note: that infinity should be \(+\infty.\))

- ganeshie8

@lgbasallote
let's say both of them start at 0...
1st week - s.k is 3... a64 is 2
2nd week - 6 - 4
3rd week - 9 - 6
4th week - 12 - 8
5th week - 15 - 10
6th week - 18 -12
.
.
.
100th week - 300 - 200
1000th week - 3000 - 2000
10000th week - 30000 - 20000
lol both must have died by now... the trick is "a 3t rate can never increase its value to 2(2t)"

- anonymous

@ganeshie8, I just said that. You essentially copied my work.

- ganeshie8

lol.. i copied your work :)

- lgbasallote

but...but... T_T
sorry @saifoo.khan seems amistre is unbeatable

- lgbasallote

but...but... T_T
sorry @saifoo.khan seems amistre is unbeatable

- anonymous

@lgbasallote, you can get above amistre. You simply cannot get to where you are double him.

- lgbasallote

yeah...what i meant lol

- saifoo.khan

@lgbasallote = Good for nothing!!! =__=
Jk

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