## Exam Style Question## Worked solutions to typical exam type questions that you can reveal gradually |

Question id: 133. This question is similar to one that appeared in a GCSE Higher paper in 2015. The use of a calculator is allowed.

On the day after one GCSE paper Twitter and the media were buzzing with comments about a particular question about Hanna's sweets. Here is our version:

Hannah has 6 orange sweets and some yellow sweets.

Overall, she has \(n\) sweets.

The probability of her taking 2 orange sweets is \(\frac13\).

Prove that: \(n^2-n-90=0\)

Hence or otherwise find \(n\).

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