Which is greater? $5.00 or the total value of all combinations of three coins you can make using only pennies, nickels, dimes, and quarters?

The answer is 5 dollars - the sum of all combinations of three coins you can make using only pennies, nickels, dimes, and quarters is $4.82, which is less than $5.00. Jennifer is correct, but her reasoning is incorrect.

To determine which is greater, $5.00 or the total value of all combinations of three coins using only pennies, nickels, dimes, and quarters, we need to calculate the total value of all possible combinations of three coins.

First, let's find the different possibilities.
1. Pennies (1 cent)
2. Nickels (5 cents)
3. Dimes (10 cents)
4. Quarters (25 cents)

We need to find all the possible combinations of the above coins with three coins in each combination.

To calculate this, we can use a systematic approach:
1. Start by choosing the first coin from the list of possibilities.
2. Then, choose the second coin from the remaining possibilities.
3. Finally, choose the third coin from the remaining possibilities.

To visualize this, let's list all the possible combinations:

1. Pennies - Pennies - Pennies: 1 cent + 1 cent + 1 cent = 3 cents
2. Pennies - Pennies - Nickels: 1 cent + 1 cent + 5 cents = 7 cents
3. Pennies - Pennies - Dimes: 1 cent + 1 cent + 10 cents = 12 cents
4. Pennies - Pennies - Quarters: 1 cent + 1 cent + 25 cents = 27 cents
5. Pennies - Nickels - Pennies: 1 cent + 5 cents + 1 cent = 7 cents
6. Pennies - Nickels - Nickels: 1 cent + 5 cents + 5 cents = 11 cents
7. Pennies - Nickels - Dimes: 1 cent + 5 cents + 10 cents = 16 cents
8. Pennies - Nickels - Quarters: 1 cent + 5 cents + 25 cents = 31 cents
9. Pennies - Dimes - Pennies: 1 cent + 10 cents + 1 cent = 12 cents
10. Pennies - Dimes - Nickels: 1 cent + 10 cents + 5 cents = 16 cents
11. Pennies - Dimes - Dimes: 1 cent + 10 cents + 10 cents = 21 cents
12. Pennies - Dimes - Quarters: 1 cent + 10 cents + 25 cents = 36 cents
13. Pennies - Quarters - Pennies: 1 cent + 25 cents + 1 cent = 27 cents
14. Pennies - Quarters - Nickels: 1 cent + 25 cents + 5 cents = 31 cents
15. Pennies - Quarters - Dimes: 1 cent + 25 cents + 10 cents = 36 cents
16. Pennies - Quarters - Quarters: 1 cent + 25 cents + 25 cents = 51 cents

Repeat the above steps for all the remaining combinations to find the total number of combinations possible.

After calculating all the possible combinations, we can add up the values of each combination to find the total value.

In this case, since we have 16 different combinations, we would add up the values of each combination:

3 + 7 + 12 + 27 + 7 + 11 + 16 + 31 + 12 + 16 + 21 + 36 + 27 + 31 + 36 + 51 = 408 cents

Now, let's compare this total value with $5.00, which can be written in cents as 500 cents.

Comparing the two values:
408 cents < 500 cents

Therefore, $5.00 is greater than the total value of all combinations of three coins using only pennies, nickels, dimes, and quarters.

The greatest coin is a quarter; If you choose three quarters, you only have $0.75, so $5.00 is greater.