## #Edexcel solution explained here

I turned on Twitter to see that “Edexcel”, whatever that is, is some kind of maths problem that students were tweeting about.

The problem is this:

The question told pupils that Hannah had a bag containing a total of n sweets of which 6 were orange. It said the chances of Hannah picking two orange sweets one after the other was one third and then said use that to prove that n²-n-90=0.

In order to see if I still had any mathematical ability left, I tried to give the problem a go.

As it happens, the problem is easy.

The probability that the first sweet is orange is 6/n. Once that is taken out of the bag, there are n-1 sweets left, 5 of which are orange. So the probability that the second sweet is orange is 5/(n-1).

We are told that the probability that the first and the second sweet are orange is 1/3. i.e.
[6/n] * [5/(n-1)] = 1/3

Cross-multiply the two sides of the equation:

6 * 5 * 3 = n * (n-1)

which rearranges to
n^2 -n – 90 =0

Simples.

What we should really be asking is why adults can’t seem to solve this problem.

Update 04-Jun-2015: So many does she have, anyway?

To work that out, we simply solve a quadratic the quadratic, which you’ll recall is:
n = [-(-1 ) + sqrt(-(-1) -4 *1 *(-90))/2
= [1 + sqrt(91)]/2 (you can ignore the negative root)
= [1+19]/2
= 10

Note that there are two roots. One of them is negative, which you can ignore, because you can’t have a negative number of sweets in a bad.

Old joke: A mathematician sees two men enter a bar. Soon after, three men leaves. He says to his friend: “when another man enters the bar, it will be exactly empty”.

Computer programmer living in Scotland.
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### 6 Responses to #Edexcel solution explained here

1. Daniel Victor says:

I worked out what n was in under two minutes – by trial and error.Proving the equation is far harder – you have to learn how to do that.

2. mcturra2000 says:

As my statistics lecturer once said to the class: I hope you all get the grades you deserve.

Needless to say, there were groans throughout the room.

3. mcturra2000 says:

Please note, I am not a teacher, and haven’t studied mathematics in many years. So I do not know what it in the curriculum. Given that I therefore know nothing, I would, in Edexcel’s defence, it seems that they were trying to test examinees’ higher-order thinking skills. This is a reasonable thing to do. Examining boards have taken a lot of flak for dumbing down their tests, so perhaps people can’t complain when they ask difficult questions.

What do the maths teachers out there think?