How many ways can you get $1.05 using only nickels, dimes, and quarters

Answer 1

I would create a table of values using
quarters, nickels and dimes

Q D N
4 0 1
3 3 0
3 2 2
3 1 4
3 0 6 Did you notice the pattern? take away 1 dime, add 2 nickels
2 5 1
2 4 3
2 3 5
2 2 7
2 1 9
2 0 11

1 8 0
1 7 2
...
1 0 16

0 10 1
0 9 3
0 8 5
...
0 0 21

Can you complete the chart and count the triples?