Getting the right mathematical representation for a riddle

Question

I haven't written any mathematical equation in years, so I struggled to solve this riddle this morning.

"2 groups, one consisting of religious people, the other of scientists, meet to discuss if Adam and Eve were the origin of mankind or if evolution led to the modern human. If one of the scientists decides to join the group of believers, the believers will have twice as many members as the scientists. If one of the believers joins the scientists, both groups will have an equal amount of members".

How would I solve this riddle mathematically?

Answer 1

Suppose the number of religious people is $x$ and the number of scientists is $y$.

"If one of the scientists decides to join the group of believers, the believers will have twice as many members as the scientists"

This means

$ x + 1 = 2 (y - 1) $

"If one of the believers joins the scientists, both groups will have an equal amount of members"

This means

$ x - 1 = y + 1 $

Now to solve these two equations, you can eliminate $x$ by subtracting the second equation from the first, this will give you

$ (x + 1) - (x - 1) = 2 (y - 1) - (y + 1) $

Simplifies, this is

$ 2 = y - 3 $

So that

$ y = 5 $

Then from either of the original equations, let's say the second equation

$ x = y + 2 $

i.e.

$ x = 7 $

Hence, the number of believers is $7$ and the number of scientists is $5$.