A man goes into a store and says, “If you give me as much money as I have with me now, I will spend $10 in your store.” The store owner agrees, and the man spends the money.
He goes into a second store and again says, “If you give me as much money as I have with me now, I will spend $10 in your store.” Again, the owner agrees, and the man spends the money.
In a third store, he repeats his proposition. The proprietor agrees, and the man spends the money.
At this point, the man has no money left. How much money did he have to begin with?

Answer:

$8.75

Step-by-step explanation:

Let x = the amount the man originally had

The man has $x and says "if you give me $x, I will spend $10."

y = amount he has after 1st proposition = x + x - 10 = 2x - 10

He repeats this procedure, now with $2x-10 in his pocket...

z = amount he has after 2nd proposition = (2x - 10) + (2x - 10) - 10 = 4x - 30

He repeats this procedure, now with $4x-30 in his pocket...but this time he is left with zero dollars...

r = amount he has after 3rd proposition = (4x-30) + (4x-30) - 10 = 8x-70 = 0

8x - 70 = 0,

x = $8.75

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