Question

(For people who like a challenge) Four waitresses in a restaurant share the tips given by customers equally every Sunday. One Sunday after work, Anne took her share from the container and left. Betty, not realising that Anne had taken her share, took her own share and left. Corrine, also unaware that Anne and Betty had taken their share, took her rightful share and left. Dawn was also unaware that the other three had taken their share, and so she took her share and left. In the end, there was $81 left in the container. How much money was there in the container at first?

Answer 1

324?

Answer 2

Before the time Dawn took her share there was \(81(\frac{4}{3})=108\).
Corrine took her share out of \(108(\frac{4}{3})=144\)
Betty took her share out of \(144(\frac{4}{3})=192\)
The original amount was \(192(\frac{4}{3})=256\).

Answer 3

Or you can just calculate is as \(81(\frac{4}{3})^4=256\).

Answer 4

I am getting 256

Let \(x\) be the amount of the tip they collected.
\(\frac{3}{4}*x\) is left after Anne took her share
\(\frac{3}{4}*\frac{3}{4}*x\) amount left after Betty took her share
\(\frac{3}{4}*\frac{3}{4}*\frac{3}{4}*x\) after Corrine took her share
\(\frac{3}{4}*\frac{3}{4}*\frac{3}{4}*\frac{3}{4}*x\) after Dawn took her share
\(\frac{3^4}{4^4}*x = 81\)
\(x = 256\)

Answer 5

THankS to ALL