December 2014 Brain Teaser Solution

Q: Tree A and tree B both have some birds.   The tree A birds tell the tree B birds “if one of you comes to our tree, our population will be the double of yours.”   The tree B birds tell the tree A birds “if one of you comes here, then our population will be equal to that of yours.” How many birds in each tree?

A:  Tree A has 7 birds and tree B has 5 birds

This can be done with guess and check or algebra

This is for statement 1)  A + 1 = 2(B – 1)

This is for statement 2)  A – 1 = B + 1

This is A in terms of B from 2) A = B + 2

Then sub into statement 1 and solve for B

B + 2 + 1 = 2B – 2

B + 3 = 2B – 2

B = 5

then can solve for A using either equation A – 1 = 5 + 1    therefore A = 7

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