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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?

Sagot :

chol25104

Answer:

$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.

A sequence or pattern in a series of numbers is a number patterns

The amount of money in coins lined up on the table is $99.19

The reason the above value is correct is as follows:

The given parameters are;

The number of pennies lined up on a table = 1,001

The coin with which every second coin is replaced with = A Nickle = 5 Cents

The coin with which every third coin is replaced with = A Dime = 10 Cents

The coin with which every second coin is replaced with = A Quarter = 25 Cents

[tex]\begin{array}{ccc}Coin \ Position&&Coin \ Value \ (Cents)\\1&&1\\2&&5\\3&&10\\4&&25\\5&&1\\6&&10\\7&&1\\8&&25\\9&&10\\10&&5\\11&&1\\12&&25\\13&&1\\14&&5\\15&&10\\16&&25\\17&&1\\18&&10\\19&&1\\20&&25\\21&&10\\22&&5\\23&&1\\24&&25\end{array}[/tex]

From the above values, we have that the first twelve coins are repetitive, therefore, the number of repeating units is the whole number part of 1,001/12 = 83, which gives;

1 + 5 + 10 + 25 + 1 + 10 + 1 + 25+ 10 + 5 + 1 + 25 = 119

The value sum of the 83 repeating 12 units = 119 × 83 = 9877

The value of the first 12 × 83 = 996 coins = 9,877 Cents

The coin in the;

997th position = 1 Cent

998th position = 5 Cent

999th position = 10 Cent

1,000th position = 25 Cent

1,001th position = 1 Cent

The total value of the coins = (9,877 + 1 + 5 + 10 + 25 + 1) Cents = 9919 Cents

9919 Cents = $99.19

The amount of money that is on the table = $99.19

Learn more about number patterns here:

https://brainly.com/question/14294944

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