How many ways can you make change for a dollar using nickels,dimes and/or quarters?

Answer 1

4q 0d 0n
3q 2d 1n
3q 1d 3n
3q 0d 5n
2q 5d 0n
2q 4d 2n
2q 3d 4n
2q 2d 6n
2q 1d 8n
2q 0d 10n
1q 7d 1n
1q 6d 3n
1q 5d 5n
1q 4d 7n
1q 3d 9n
1q 2d 11n
1q 1d 13n
1q 0d 15n
0q 10d 0n
0q 9d 2n
0q 8d 4n
0q 7d 6n
0q 6d 8n
0q 5d 10n
0q 4d 12n
0q 3d 14n
0q 2d 16n
0q 1d 18n
0q 0d 20n

29 different combinations.

Answer 2

n = number of nickels
d = number of dimes
q = number of quarters

100 (cents) = 5n + 10d + 25q where n,d,q are positive integers
20 = n + 2d + 5q
n = 20 - 5q - 2d

There are only 5 scenarios for q (0, 1, 2, 3, 4). Therefore, you have 5 equations where n >= 0

n = 20 - 5(0) - 2d = 20 - 2d >= 0
n = 20 - 5(1) - 2d = 15 - 2d >= 0
n = 20 - 5(2) - 2d = 10 - 2d >= 0
n = 20 - 5(3) - 2d = 5 - 2d >= 0
n = 20 - 5(4) - 2d = 0 - 2d >= 0

for each equation, determine the possible values of d:
when q = 0, 20 - 2d >= 0, d <= 10 (11 ways)
when q = 1, 15 - 2d >= 0: d <= 7 (8 ways)
when q = 2, 10 - 2d >= 0: d <= 5 (6 ways)
when q = 3, 5 - 2d >= 0: d <= 2 (3 ways)
when q = 4, 0 - 2d >= 0: d <= 0 (1 way)

Total = 29 ways

Answer 3

The answer is 29 different ways.

This can be stated as:
= (# of ways with 4 quarters) + (# of ways with 3 quarters) + (# of ways with 2 quarters) + (# of ways with 1 quarters) + (# of ways with 0 quarters)
= 1 + 3 + 6 + 8 + 11
= 29

Answer 4

Are you studying combination theory, or just bored? If you give me the dollar, I will try it out for you.

Answer 5

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