Question

Nick has $5, $20, and $100 bills that total 17 bills. He exchanges all his $5 bills for $1 bills, then all his $20 bills for $5 bills, and finally all his $100 bills for $20 bills. At the end, Nick has a total of 77 bills. How many $20 bills did Nick have originally? Assume that each exchange preserves the total dollar amount of Nick’s money.

Answer 1

8

Explanation:

Key to this question is assume that each exchange preserves the total dollar amount of Nick’s money.

If He exchanges all his $5 bills for $1 bills, it means that a $5 bill will result in 5 $1 bills as such, if he had x number of $5 bill, after the exchange, he would have 5x $1 bills.

then all his $20 bills for $5 bills, it means that for each $20 bill, he gets 4 $5 bills which means that if he had y number of $5 bills, after the exchange, he would have 4y $5 bills.

and finally all his $100 bills for $20 bills, then he must have received 5 $20 bills for each $100 such that if he had z number of $100 bills before the exchange, he would have 5z number of $20 bills after the exchange. Given that originally he had 17 bills and later 77 bills then

x + y + z = 17

5x + 4y + 5z = 77

Multiplying the first equation by 5,

5x + 5y + 5z = 85

5x + 4y + 5z = 77

subtract 2 from 1

y = 8