Change Algebra- Deadline: When the expiration ends!;)?

Question

Find all the $0.50 with our current currency (USD coins). For example, one coin can be used-- a fifty-cent piece-to make $0.50. Two quarters also make fifty cents. Fifty pennies make fifty cents and so on until all solutions are found. Next, write out all your solutions in algebraic form. For example: 2d + 30p = 0.50 when d=0.10 adn p= 0.01. Once you have found all the combinations for $0.50 and have written all of the solutions in algebraic form, do the same for $0.75; and again find all the solutions in algebraic form.
Any annoyance comments will be given a low ratig, as with abusive comments and comments off subject.

Answer 1

50 cents:
one half dollar (1h = .50)
2 quarters (2q = .50)
1 quarter, 2 dimes, 1 nickel (1q + 2d + 1n = .50)
1 quarter, 2 dimes, 5 pennies (1q + 2d + 5p = .50)
1 quarter, 1 dime, 3 nickels (1q + 1d + 3n = .50)
1 quarter, 1 dime, 2 nickels, 5 pennies (1q + 1d + 2n + 5 p = .50)
1 quarter, 1 dime, 1 nickel, 10 pennies (1q + 1d + 1n + 10p = .50)
1 quarter, 1 dime, 15 pennies (1q + 1d + 15p = .50)
1 quarter, 5 nickels (1q + 5n = .50)
1 quarter, 4 nickels, 5 pennies (1q + 4n + 5p)
1 quarter, 3 nickels, 10 pennies (1q + 3 n + 10p = .50)
1 quarter, 2 nickels, 15 pennies (1q + 2n + 15p = .50)
1 quarter, 1 nickel, 20 pennies (1q + 1n + 20p = .50)
1 quarter, 25 pennies (1q + 25p = .50)
5 dimes (5d = .50)
4 dimes and 2 nickels (4d + 2n = .50)
4 dimes, 1 nickel and 5 pennies (4d + 1n +5p = .50)
4 dimes, 10 pennies (4d +10p = .50)
3 dimes, 4 nickels (3d + 4n = .50)
3 dimes, 3 nickels, 5 pennies (3d + 3n + 5p = .50)
3 dimes, 2 nickels, 10 pennies (3d + 2n + 10p = .50)
3 dimes, 1 nickel, 15 pennies (3d + 1n + 15p = .50)
3 dimes, 20 pennies (3d + 20p = .50)
2 dimes, 6 nickels (2d + 6n = .50)
2 dimes, 5 nickels, 5 pennies (2d + 5n + 5p = .50)
2 dimes, 4 nickels, 10 pennies (2d + 4n + 10p = .50)
2 dimes, 3 nickels, 15 pennies (2d + 3n + 15p = .50)
2 dimes, 2 nickels, 20 pennies (2d + 2n + 20p = .50)
2 dimes, 1 nickel, 25 pennies (2d + 1n + 25p = .50)
2 dimes, 30 pennies (2d + 30p = .50)
1 dime, 8 nickels (1d + 8n = .50)
1 dime, 7 nickels, 5 pennies (1d + 7n +5p = .50)
1 dime, 6 nickels, 10 pennies (1d + 6n + 10p = .50)
1 dime, 5 nickels, 15 pennies (1d + 5n + 15p = .50)
1 dime, 4 nickels, 20 pennies (1d + 4n + 20p = .50)
1 dime, 3 nickels, 25 pennies (1d + 3n + 25p = .50)
1 dime, 2 nickels, 30 pennies (1d + 2n + 30p = .50)
1 dime, 1 nickel, 35 pennies (1d + 1n + 35 p = .50)
1 dime, 40 pennies (1d + 40p = .50)
10 nickels (10n = .50)
9 nickels, 5 pennies (9n + 5p = .50)
8 nickels, 10 pennies (8n + 10p = .50)
7 nickels, 15 pennies (7n + 15p = .50)
6 nickels, 20 pennies (6n + 20p = .50)
5 nickels, 25 pennies (5n + 25p = .50)
4 nickels, 30 pennies (4n + 30p = .50)
3 nickels, 35 pennies (3n + 35p = .50)
2 nickels, 40 pennies (2n + 40p = .50)
1 nickel, 45 pennies (1n + 45p = .50)
50 pennies (50p = .50)

Hope you see the pattern that was used. Now you use the same type of pattern for .75.

Answer 2

You're only going to get then all if you do it in order. Say, for instance, you start from the highest to the lowest.

1 half-dollar

No more half-dollars can be used, so drop to the next largest coin:

2 quarters
1 quarter, two dimes, and a nickel
1 quarter, two dimes, and five pennies
1 quarter, one dime, and three nickels
1 quarter, one dime, two nickels and five pennies
1 quarter, one dime, one nickel and ten pennies
1 quarter, one dime, fifteen pennies
1 quarter, five nickels
1 quarter, four nickels, five pennies
1 quarter, three nickels, ten pennies
1 quarter, two nickels, fifteen pennies
1 quarter, one nickel, twenty pennies
1 quarter, twenty-five pennies

Now drop the quarter and move on - you get the idea. There are a bunch of possibilities, and seventy-five cents will be even worse.

Good luck.

Answer 3

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