There are 1001 pennies lined up on a table. I come along and replace every 2nd coin with a Nickle. Then, replace every 3rd coin with a Dime. Finally, I replace every 4th coin with a Quarter. How much money is on the table?

$99.19

Step-by-step explanation:

Problem:

On a table there are 1001 pennies lined up in a row. I come along and replace every second coin with a nickel.  Then I replace every third coin with a dime.  Finally, I replace every fourth coin with a quarter.  How much money is on the table now? Why is twelve important?

Solution:

Our first step was to make a line of pennies (as long as possible) in order to see if we could figure out a pattern that would help us determine the total amount of money on the table.  

Then we went through and replace every second coin with a nickel.

Then we went through and replaced every third coin with a dime.

Then we went through and replaced every fourth coin with a quarter.

As a group we then tried to decipher if there was a pattern that would help us determine the total value of coins.  We then noticed that there was a pattern of twelve coins.

= $1.19

= $1.19

= $1.19

We determined the number of times the pattern of twelve coins repeated in the 1001 coins:

1001 ÷ 12 = 83 R5

Since we knew that the pattern repeated itself 83 full times and each time the dollar value is $1.19 we counted to determine the cost of the first 996 coins.

$1.19 X 83 = $98.77

Then we added the remaining 5 coins, which cost $0.42

$98.77 + $0.42 = $99.19

Therefore, there is a total of $99.19 on the table.

Since, the lowest common multiple of 2, 3, and 4 is 12, the pattern will repeat itself every 12th coin.