# 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

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#### HallsofIvy

Science Advisor
Homework Helper
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- plz show). But im guessing that n is greater than 3/5 so it CANT be right?

#### danago

Gold Member
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 thats 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 cant have 1/2 a ball...

am I right or am I right

Last edited:

#### thomas49th

Okay here is the rest of the question

#### Hootenanny

Staff Emeritus
Science Advisor
Gold Member
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

Staff Emeritus
Science Advisor
Gold Member
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 ive 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 cant have 3.5 balls

#### Hootenanny

Staff Emeritus
Science Advisor
Gold Member
All sounds good to me, well done