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Could you answer this GCSE maths question?


Chris Sheppard
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Just read about this and can't help but think kids are getting it easier than we did.

 

https://uk.news.yahoo.com/tricky-gcse-exam-paper-trends-twitter-083604261.html#F13AwBR

 

(Copied from the link above)

This is the question:

There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow.

Hannah takes a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet.

The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0

 

I don't profess to be a maths whiz, and left school over 15 years ago, but it took all of about a minute to work out (maybe I've over simplified it, or even got it wrong?)

 

n squared - n - 90 = 0

 

so,

 

n squared - n = 0 + 90 (add 90 to each side)

 

so

 

n squared = 90 + n (add n to each side)

 

bearing in mind there can't be any part sweets, a quick try of n = 9 didn't work (9 x 9 being only 81)

 

so tried n = 10

 

10 squared = 100

 

or 10 x 10 = 90 +10

 

Maybe I've missed summat, but surely that shows what they ask?

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n does indeed work out to be 10

 

so the odds of first sweet being orange is 6/10

 

and the odds of the second being orange is 5/9

 

therefore the odds of the first 2 being orange is 6/10 times 5/9 which is 30/90 or 1/3.

 

Buggered if I can work out how they arrived at " n squared - n -90=0 "

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I left school over thirty years ago and would have absolutely no idea how to go about answering that question whatsoever. ( I have an O level grade B and a GCSE grade 4 in maths). I've been running my own business since the age of 23 by the way, so if its a pounds and pence equation I'm sure it would be a doddle :biggrin:

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Maybe I've missed summat, but surely that shows what they ask?

 

They are not asking you find the value of n,but are asking you to ,write an equation for the probability , that can be simplified to the equation given.

 

30 years ago I would have simply replaced 5/9 with 5/n-1 and solved it.

 

I guess its harder once you've worked out the answer.

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