One day you line up 240 quarters on a table You decide for f

One day you line up 240 quarters on a table. You decide, for fun, to replace every second coin with a dime. You continue swapping coins and replace every third coin with a nickel. Finally, due to the immeasurable fun you are having, you replace every fourth coin with a penny. After all of your fun time coin replacing, what is the total value of the remaining coins?

Solution

quarter = 0.25 dollars

dime = 0.10 dollars

nickel = 0.05 dollars

penny = 0.01 dollars

The coins are replaced every 2nd.3rd and 4th instant, the LCM of all these numbers is equal to 12

Hence each 20 sets of 12 coins will have the same value

Initially - QQQQQQQQQQQQ

After replacing first step - QDQDQDQDQDQD

Second step - QDNDQNQDNDQN

Last step - QDNPQNQPNDQP

Cost of 12-set coin = cost of 4 quarters + cost of 2 dimes + cost of 3 nickels + cost of 3 pennies

=> 4 * 0.25 + 2 * 0.10 + 3 * 0.05 + 3 * 0.01

=> 1 + 0.20 + 0.15 + 0.03

=> 1.38$

Total cost = cost of 20 such sets

=> 20 * $1.38

=> $27.6