Question 19 - quadratic probility problem

[thomas49th]

a) (i) (x-14)(2x-7)
(ii) x = 14 or x = 3.5

b)
i) \frac{7}{n+7}
ii) Take n to be 8

\frac{7}{8+7}
\frac{7}{15} that DOESN'T round down to \frac{2}{5}

Is that all correct so far?
If so I will post the next (really hard) question)...

Thanks

 

[HallsofIvy]

Why take n to be 8? Nothing is said about any value for n.
If 7/(n+7)= 2/5, SOLVE for n. What happens?

 

[thomas49th]

\frac{7}{n+7} = \frac{2}{5}

cross multiply!

\frac{35}{2n+14}

now where?

 

[Mystic998]

Um...you're leaving out the equality part of the equation. Solve for n.

 

[Mystic998]

Alternatively, you can note that you have 35/(2n + 14) = 1. 35 is odd. 2n + 14 is even. Strange, isn't it?

 

[thomas49th]

uh? How does that equal 1?

 

[Mystic998]

Look, you're essentially supposed to say, "Suppose Bill is right. Suppose 7/(n + 7) = 2/5. Then such and such would follow." Why would the conclusion be a problem?

 

[thomas49th]

\frac{35}{2n+14} = 1

now I need to get N on it's own (don't know how- please show). But I am guessing that n is greater than 3/5 so it CANT be right?

 

[danago]

Multiply both sides of the equation by 2n + 14, so you end up with:

35 = 2n + 14

 

[thomas49th]

silly me...

2n = 35-14
n = 10.5
EDIT: Which as a fraction is 10/1/2 which DOESN'T equal 2/5...am i right yet. I doubt that's right...

 

[Mystic998]

You're getting there. What's the problem with n being 10.5. Look at your original assumptions. What are you tacitly assuming about the original n balls?

 

[thomas49th]

you can't have 1/2 a ball...

am I right or am I right

 

[thomas49th]

Okay here is the rest of the question

 

[Hootenanny]

Okay, what are your ideas on part (c)?

 

[thomas49th]

(probability of taking white x probability of taking yellow) + (probability of taking yellow x probality of taking white)

Is that somthing to go from?

Thanks

 

[Hootenanny]

Yes, I'd go with that.

 

[thomas49th]

I got it down now to \frac{14n}{2n^{2}+28n+98} = \frac{4}{9}

is that right so far?

EDIT: is the question is says -28n but I've got +28n


EDIT 2: O no it must be this so far

\frac{14n}{n^{2}+14n+49} = \frac{4}{9}

 

[thomas49th]

got it!

\frac{4n^{2} + 56n + 196}{2} = \frac{14n * 9}{2}
\2n^{2} + 28n + 98 = 68n


\2n^{2} - 35n + 98 = 0

 

[thomas49th]

and the answer to d must be 1/9
x must be 14 as you can't have 3.5 balls

 

[Hootenanny]

All sounds good to me, well done