### Brain Teasers

# Sabrina and Samantha

Sabrina gave Samantha as many dollars as Samantha started out with. Samantha then gave Sabrina back as much as Sabrina had left. Sabrina then gave Samantha back as many dollars as Samantha had left, which left Sabrina broke and gave Samantha a total of $80.00. How much did Sabrina and Samantha have at the beginning of their exchange?

### Answer

Sabrina had $50 and Samantha had $30.This can be solved by setting up two simultaneous equations, but it's easier just to work backwards:

At each step, the person who is receiving the money gets the amount that they were already holding. In other words, they double their money.

Therefore, just before the last exchange, Samantha must have had $40 and was given another $40 to get to her total of $80.

Just before the second exchange, Sabrina must have had half of her $40. Therefore, Sabrina had $20 and Samantha had $60.

After the first exchange Samantha doubled her money, so she must have had $30 before the exchange, leaving Sabrina with $50 at the start.

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