1180.62 – Robins Here and There

Look out your classroom window! See the group of robins on the ground? And the second group in a tree? If you look carefully, you will notice that if one bird flies from the tree to the ground, the number of robins in each group will be equal. However, if one bird flies from the ground to the tree, then the group in the tree will have twice as many robins as the group on the ground.

How many robins in each group?

Solution

There are 7 robins in the tree and 5 on the ground.

If xx robins are in the tree and yy are on the ground, then x - 1 = y + 1, or x = y + 2. Now,

x+1=2(y−1)y+3=2y−2 \begin{aligned} x + 1 &=& 2(y - 1) \\ y + 3 &=& 2y -2 \end{aligned}

hence y=5y = 5 and x=7.x = 7.