Question 578994: How many ways can you make change for $20 using only quarters and dimes?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Suppose we fix the number of quarters. Then the number of dimes is uniquely determined (e.g. if we have 4 quarters, we must have 190 dimes).
However, the number of quarters must be a multiple of 2 (this is because 25 is not divisible by 10, but 50 is). Therefore the possibilities for the number of quarters are {0,2,4,6,...,80} (since $20 = 80 quarters). There are 41 numbers in the set {0,2,4,6,...,80} so there are 41 ways.
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