SOLUTION: You have $100 and want to buy 100 items priced at $10, $3 and .50. What is the combination of items purchased when you must buy at least 1 of each?

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Question 340654: You have $100 and want to buy 100 items priced at $10, $3 and .50. What is the combination of items purchased when you must buy at least 1 of each?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let A be the number of $10 parts, B $3 parts, C $0.50 parts.
1.A%2BB%2BC=100
.
.
.
10A%2B3B%2B0.5C=100
2.20A%2B6B%2BC=200
From eq. 1,
C=100-A-B
Substitute into eq. 2,
20A%2B6B%2B100-A-B=200
19A%2B5B=100
The equation can only be satisfied when 19A is a multiple of 5.
In becomes a multiple of 5 when highlight%28A=5%29.
19%285%29%2B5B=100
95%2B5B=100
5B=5
highlight%28B=1%29
Then
C=100-1-5
highlight%28C=94%29