Shopping for maths: How much money did he start with?

[Kwhit]

"A man goes into a shop and says to the owner, 'give me as much money as I have with me and I will spend $16.00'. The shopkeeper agrees so the man does the same thing in a second and third shop. After his third purchase he has no money left. How much money did he start with?"

Who can work this one out?

 

[HallsofIvy]

Work backwards. At the third shop he was given as much money as he had, spent $16, and had nothing left. So after having been given "as much money as he had" he must have had $16 so he must have come into the store with $16/2= $8 and been given $8.

Now go back to the second store. He was given as much money as he had, spent $16, and had $8 left. Before spending the $16 he must have had $16+ $8= $24. That means he came into the store with $24/2= $12 and been given $12.

Finally, the first store. He was given as much money as he had, spent $16, and had $12 left. How much money did he have before spending the $16? How much was he given and how much did he come into the store with?