Question

A tree is losing its leaves. 2/3 fall off in the first week, 2/3 of those remaining fall off in the second week, and 2/3 of those remaining fall off in the third week. Now there are 37 leaves. How many leaves did the tree start with?

Answer 1

After first week remains $1-\frac{2}{3}=\frac{1}{3}$ leaves

After second week remains $\frac{1}{3}-\frac{1}{3}\frac{2}{3}=\frac{1}{9}$ leaves

After third week remains $\frac{1}{9}-\frac{1}{9}\frac{2}{3}=\frac{1}{27}$ leaves

Let x be the number of the leaves, the tree starts with.

We have: $\frac{x}{27}=37$

So, the tree starts with $x=27*37=999$ leaves.