Discussion question

can you please answer this questionBoris has an incredible coin changing machine. When he puts in a quarter, it returns five nickels; when he puts in a nickel, it returns five pennies; and when he puts in a penny, it returns five quarters. Boris starts with just one penny. Which of the following amounts could Boris have after using the machine repeatedly?
3.63$
5.13$
6.30$
7.45$
9.07$
the given solution i feel is wrong and i am quite confused. Thank you so much!

What was the answer it gave you and what did you get? I got 7.45

here's my reasoning. Basically your coin value stays the same, except on the penny to quarter transaction, in which your coin value is multiplied by 125. For example, one penny turns into 125 cents, 2 pennies turns into 250 cents. Thus, at any given point, Boris must have 125x.

@KevinLi You have the right idea! The key is that the only time the amount of money changes is when Boris trades in a penny for 5 quarters... But, does this always mean that the amount of money is multiplied by 125?
Here's an example: If I have two pennies and a nickel, that's 7 cents. If I trade in one penny for 5 quarters, i'd have one penny, one nickel, and five quarters, and that's 131 cents. Hm, my money didn't exactly get multiplied by 125. What exactly changed?
Once you figure that out, you'll get the answer in no time!