Question

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.

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.