Trivia?? How many ways can you make change for a fifty dollar bill
Favorites|Homepage
Subscriptions | sitemap
HOME > > Trivia?? How many ways can you make change for a fifty dollar bill

Trivia?? How many ways can you make change for a fifty dollar bill

[From: ] [author: ] [Date: 12-06-12] [Hit: ]
x has to be a multiple of 5.So,z = 0 ==> k + y = 10 has 9 positive.z = 1 ==> k + y = 8 has 7 non-neg.z = 2 ==> k + y = 6 has 5 non-neg.z = 3 ==> k + y = 4 has 3 non-neg.......
If you have ones, fives and tens. Assuming that there are enough of each denomination of each currency in the drawer. How many different ways can you make change for a $50 if you must use at least one bill of each kind?

-
We want to solve for positive integer solutions
x + 5y + 10z = 50.

Plainly, x has to be a multiple of 5.
So, writing x = 5k for some positive integer k yields
5k + 5y + 10z = 50 ==> k + y + 2z = 10

This can be enumerated from here:
z = 0 ==> k + y = 10 has 9 positive. integer solutions
z = 1 ==> k + y = 8 has 7 non-neg. integer solutions
z = 2 ==> k + y = 6 has 5 non-neg. integer solutions
z = 3 ==> k + y = 4 has 3 non-neg. integer solutions
z = 4 ==> k + y = 2 has 1 non-neg. integer solutions
z = 5 (and higher): no non-neg. integer solution.

Altogether, there are 1 + 3 + 5 + 7 + 9 = 25 ways.

I hope this helps!
1
keywords: change,you,How,fifty,make,can,dollar,many,bill,Trivia,ways,for,Trivia?? How many ways can you make change for a fifty dollar bill
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .