Question 937824: suppose you have a currency named miso in three denominations 1 miso , 50 miso and 10 miso. in how many ways can you pay a bill of 107 miso
a) 16
b) 17
c)18
d)19
e)20
Answer by Edwin McCravy(20062)   (Show Source):
You can put this solution on YOUR website! 1 miso , 50 miso and 10 miso. in how many ways can you pay a bill of 107 miso
x + 10y + 50z = 107
Since 107 ends in a 7 and 10y and 50z will have to end in a 0,
x must end in a 7, so x = 10k + 7
(10k + 7) + 10y + 50z = 107
10k + 10y + 50z = 100
k + y + 5z = 10
k + y = 10 - 5z
if z = 0, then
k + y = 10 - 5(0)
k + y = 10
k can be any integer from 0 to 10, inclusive, and y can
be chosen to make up the difference That's 11 ways
if z = 1, then
k + y = 10 - 5(1)
k + y = 5
k can be any integer from 0 to 5, inclusive, and y can
be chosen to make up the difference That's 6 ways.
if z = 2, then
k + y = 10 - 5(2)
k + y = 0
k and y can only be 0. That's 1 more way.
Total number of ways: 11+6+1 = 18 ways.
FYI, here they all are:
1. 107 ones.
2. 1 ten and 97 ones.
3. 2 tens and 87 ones.
4. 3 tens and 77 ones.
5. 4 tens and 67 ones.
6. 5 tens and 57 ones.
7. 6 tens and 47 ones.
8. 7 tens and 37 ones.
9. 8 tens and 27 ones.
10. 9 tens and 17 ones.
11. 10 tens and 7 ones.
12. 1 fifty and 57 ones.
13. 1 fifty, 1 ten and 47 ones.
14. 1 fifty, 2 tens and 37 ones.
15. 1 fifty, 3 tens and 27 ones.
16. 1 fifty, 4 tens and 17 ones.
17. 1 fifty, 5 tens and 7 ones.
18. 2 fifties and 7 ones.
Edwin
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