Question 825247: Break one one hundred doller Bill into forty bills
Answer by josgarithmetic(39794)   (Show Source):
You can put this solution on YOUR website! Not being sure if a formal process for this is known, you can use twenty of five-dollar bills to equal 100 dollars. Each five dollar bill broken into ones give you five bills. Take ten of your five dollar bills and they translate into 20 each of one dollar bills.
50 each of $1 = $50.
10 each of $5 = $50.
That is excess of 20 bills.
40 each of $1 = $40
2 each of $5 = $10
10 each of $5 = $50;
We could go on like this, but take another extreme.
Start with 100 each of $1 bills.
Change to this:
80 each of $1 bill = $80
1 each of $20 bill = $20
60 each of $1 = $60
2 each of $20 = $40
40 each of $1 = $40
3 each of $20 = $60
Some amounts of tens and fives bills may be very helpful now.
30 each of $1 = $30
2 each of $10 = $20
3 each of $20 = $60
30 each of $1 = $30
2 each of $10 = $20
6 each of $10 = $60
Two more bills are needed.
This combination works. Forty bills, total money:
30*1+4*5+6*10=30+20+60=100
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30 each of $1 bills
4 each of $5 bills
6 each of $10 bills
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MAYBE ALGEBRA METHOD
A linear algebra, linear systems way might work, too, but not sure how many variables you would use. three or four variables?
'
w, x, y, z for bill count of bills for values at 1, 5, 10, 20.
Accounting for money, w+5x+10y=100, assuming you might be avoiding any $20 bills;
Accounting for bill count, w+x+y=40.
You would need to assume or pick an arbitrary variable to be assumed constant and try to solve the system in terms of that picked variable.
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