AIBU to ask for GCSE maths help

[innkeeper]

Wonder if anyone can help. I know the answer is 15 but not how to get there! X counters in jar. 7 are red. One removed and one the table. Another removed and on table. Probability of two being red is 1/5. What is x? Please help fraught mother and son! Thanks in advance

Can you post a picture of the question? Sometimes it helps to see it written

Solve 7/x multiplied by 6/(x-1) equals 1/5. I think you'll end up with a quadratic equation to solve.

This is an A* (grade 8/9 question so only bother with it if thats the grade they are working towards or they will find it too hard to solve

Solution

First, draw a probability tree, with the first branch representing the first countr to be withdrawn. The top being probability(red) which is 7/x, and the bottom being prob(not red) which you don't need to calculate.
The second branch of the prob tree represents the second counter being taken out of the jar. The top prob(red) will be now 6/x-1. This is because now there are only 6 red counters in the jar, and x-1 counters altogethr now.
To find the prob (both red), multiply the probs together,
So 7/x x 6/x-1 = 1/5.
Multiply left side out and simplify and rearrange to get
X squared - x - 210 = 0
Solve (by factorising) to get (x-15)(x+14) =0
To get x=15 or x=-14
-14 doesn't work here so x=15

This works...

Or if you don't like quadratics you can do it by prime factor decomposition with a bit if trial and error at the end.

The examiner is probably just looking for a quadratic though. So maybe best not to over complicate it.

Thanks so much - he understands it now. Much appreciated