Question

There are two trees in a garden (A and B) and on both trees are some birds.

The birds in tree A say to the birds in tree B, "If one of you comes to our tree, then our population will be double that of yours."
But the birds in tree B counter, "If one of you comes here, then our population will be equal to that of yours."

How many birds are in each tree? (before the birds move around)

p.s. Please show your work

Answer 1

"If one of you comes to our tree, then our population will be double that of yours."

So
`A+1 =2* (B-1) A+1 = 2B - 2`

"If one of you comes here, then our population will be equal to that of yours."


`A-1 = B+1`

Rearranging these to make A the subject gives:


`A = 2B-3`

`A = B +2`

Then solve for B:


`2B - 3 = B + 2 B = 5`

Substitute B back in to an equation:


`A = B + 2 A = 5 + 2 A = 7`

So there are seven birds in A, and 5 birds in B