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
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)
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”.
Edit 25-Jun-2015: Added picture