# Coins

first, what coins are available :
p = Penny
north = Nickel
vitamin d = Dime

q = quarter
heat content = Half dollar

Some combination of these coins must equal \$ 1.00, consequently

.01p + .05n + .10d + .25q + .5h = \$ 1.00
p + n + d + q + planck’s constant = 19

Questions we should consider :

1. Can we achieve a solution with only one type of coin ? No .
2. 100 pennies = \$1

3. 20 nickels = \$1

4. 10 dimes = \$1

5. 4 quarters = \$1

6. 2 half dollars = \$1

7.

What happens if we use pennies ?

1. Pennies must be used in multiples of 5, otherwise we can not reach a whole issue
2. Since we can not use 20 pennies, we can merely use 5, 10, or pennies

If we use 5 pennies

1. .05n + .10d + .25q + .5h = \$0.95

2. n + d + q + h = 14

1. 14 nickels only equals \$ 0.70, so we need to reduce the number of nickels
2. If we use 12 nickels
3. .10d + .25q + .5h = \$0.35

4. d + q + h = 2

now consider the other coins

1. It seems clear up from this steer that we will need 1 dime bag and 1 quarter
2. .01(5) + .05(12) + .10(1) + .25(1)= \$1.00

Are there other combinations that can be made using 5 pennies ?

Let ’ s consider nickels :

1. 18 nickels = \$ 0.90
2. We can only use 1 mint and it must equal \$ 010, so in this font it must be 1 dime bag
3. .05(18) + .10(1) = \$1.00

4.

now let ’ s look at dimes :

1. 9 dimes = \$ 0.90
2. We must use 10 more coins and they can ’ t sum to more than \$ 0.10
3. 1 nickel and 5 pennies sums to \$ 0.10, but only requires 6 coins
4. consequently, the only option is to use 10 pennies
5. .01(10) + .10(9) = \$1.00

nowadays let ’ s look at quarters :

1. 3 quarters = \$ 0.75
2. We must use 16 more coins and they can ’ metric ton sum to more than \$ 0.25
3. 2 dimes and 1 nickel sums to \$ 0.25, but only requires 3 coins
4. 15 pennies and 1 dime has the adjust total and correct number of coins
5. .01(15) + .10(1) + .25(3)= \$1.00

6.

7. 1 quarter = \$ 0.25
8. We must use 18 more coins and they can ’ t sum to more than \$ 0.85
9. 2 dimes and 1 nickel sums to \$ 0.25, but lone requires 3 coins
10. 15 pennies and 1 dime has the right sum and discipline number of coins
11. .01(10) + .05(1) + .10(7) + .25(1)= \$1.00

now let ’ s count at half dollars :

1. 1 half dollar = \$ 0.50
2. We must use 18 more coins and they can ’ deoxythymidine monophosphate sum to more than \$ 0.50
3. 15 pennies and 1 dime bag sums to \$ 0.25, but we can ’ triiodothyronine reach \$ 1 with merely 2 coins
4. 10 pennies, 1 dime bag, and 1 nickel sums to \$ 0.25, but does not use enough coins
5. .01(15) + .10(1) + .25(3)= \$1.00

6.

Does adding the equations help ?

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Category : Finance