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Amy visits three stores.At the first store she spends half of her money plus $20, at the second store she spends half the money she has left plus $10 and at the third store she spends half of what she has left plus $20. She is now out of money. How much money did Amy start out with?

Please help.

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1 answer
  1. starting value ...... x
    money spent at store #1 = x/2 + 20
    after first store, amount left = x - (x/2+20) = x/2 - 20
    amount spent at second store = (1/2)(x/2 - 20) + 10 = x/4
    amount left = x/2 - 20 - x/4 = x/4 - 20

    third store she spent (1/2)(x/4 - 20) + 20 = x/8 + 10
    to have nothing left,
    x/4 - 20 - (x/8 + 10) = 0
    x/8 = 30
    x = 240

    checking this:
    amount spent at 1st store = (1/2)(240) + 20 = 140
    leaving her with 100
    amount spent at 2nd store = (1/2)(100) + 10 = 60
    leaving her with 40
    amount spent at 3rd store = (1/2)(40) + 20 = 40
    amount left over = 40-40 = 0

    x = 240 is verified.

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