Six hundred pennies are placed in a row. If every other penny is replaced by a nickel and every third coin is replaced by a quarter, what is the final value of the 600 coins?
600 pennies = $6.00
after replacement by a nickel, there are 300 pennies and 300 nickels.
Value = 300*0.01 + 300*0.05 = $18.00
Finally, the replacement by quarters every third coin means that one-third of the nickels and one-third of the pennies will be replaced by quarters.
Think of the replacement process: the first one encountered is a penny, the next one is a nickel, the third one is a penny, .....
In the end, there will be
200 pennies,
200 nickels, and
200 quarters.
Total value = 200(0.01+0.05+0.25)=$62.00
Well, let's do some math with a touch of humor!
First, let's replace every other penny with a nickel. So, we'll have 300 pennies left and replace the other 300 with nickels. That gives us 300 pennies and 300 nickels.
Now, let's replace every third coin (which is now a nickel) with a quarter. Since we have 300 nickels, let's divide that by 3 to see how many coins we will replace. Simple math, 300 divided by 3 is 100. So, we'll replace 100 nickels with quarters. That leaves us with 200 nickels and 100 quarters.
Now let's calculate the value of these coins! A penny is worth 1 cent, a nickel is worth 5 cents, and a quarter is worth 25 cents.
So, the value of the 200 nickels will be 200 * 5 cents, which equals 1000 cents. And the value of the 100 quarters will be 100 * 25 cents, which equals 2500 cents.
Now, we just need to add them up! So, 1000 cents + 2500 cents equals 3500 cents.
But wait! We still need to convert it back into dollars. So, let's divide by 100. 3500 cents divided by 100 equals 35 dollars.
Ta-da! The final value of the 600 coins, after replacing every other penny with a nickel and every third coin with a quarter, is 35 dollars.
To solve this problem, let's break it down step-by-step:
Step 1: Calculate the number of nickels.
Every other penny is replaced by a nickel, so the number of nickels is half the number of pennies: 600 / 2 = 300 nickels.
Step 2: Calculate the number of quarters.
Every third coin is replaced by a quarter. To find how many quarters there are, divide the number of pennies by 3: 600 / 3 = 200 quarters.
Step 3: Calculate the value of the pennies.
The value of a penny is $0.01, so the total value of the pennies is 600 * $0.01 = $6.
Step 4: Calculate the value of the nickels.
The value of a nickel is $0.05, so the total value of the nickels is 300 * $0.05 = $15.
Step 5: Calculate the value of the quarters.
The value of a quarter is $0.25, so the total value of the quarters is 200 * $0.25 = $50.
Step 6: Calculate the final value of all the coins.
Add up the values of the pennies, nickels, and quarters to find the final value of the 600 coins:
$6 + $15 + $50 = $71.
Therefore, the final value of the 600 coins is $71.
To solve this problem, we need to calculate the final value of the 600 coins by replacing every other penny with a nickel and every third coin with a quarter.
Step 1: Calculate the number of coins that will be replaced by a nickel:
There are 600 pennies in total, so every other penny means we need to replace half of them. 600 divided by 2 equals 300 coins.
Step 2: Calculate the number of coins that will be replaced by a quarter:
There are 600 coins in total, so every third coin means we need to replace one-third of them. 600 divided by 3 equals 200 coins.
Step 3: Calculate the remaining number of coins:
To find the remaining number of coins, subtract the number of replaced coins from the initial total. Initial total = 600 coins, replaced coins = 300 (nickels) + 200 (quarters) = 500 coins. So, the remaining number of coins is 600 - 500 = 100 coins.
Step 4: Calculate the total value of each type of coin:
A nickel is worth 5 cents, so 300 nickels (replacing the pennies) have a total value of 300 * 5 = 1500 cents.
A quarter is worth 25 cents, so 200 quarters have a total value of 200 * 25 = 5000 cents.
The remaining 100 coins are still pennies, so their value remains the same, i.e., 100 cents.
Step 5: Calculate the final total value:
Add up the total value of each type of coin: 1500 cents (nickels) + 5000 cents (quarters) + 100 cents (pennies) = 6600 cents.
Therefore, the final value of the 600 coins is 6600 cents.