Beach Day by Rodger Bliss
July 2024

Sabrina is Broke

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?

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3 guesses to Sabrina is Broke

  • Melody

    Sabrina started with $50 and Samantha started with $30

    Sab Sam
    50 30 Starting
    -30 +30 Sabrina gives as many as Sam started with
    —- —-
    20 60
    +20 -20 Sam gives Sabrina back as much as Sabrina had left
    —- —–
    40 40
    -40 +40 Sabrina then gave Sam back as many dollars as Sam had left
    —- —–
    0 80 Leaving Sabrina broke and Samantha at $80

  • Dude

    Correct Melody.

    Sabrina had 50 dollars and Samantha had 30 dollars.

    You are today’s winner.

  • Annie

    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.