Question 1044296: You are making stacks of coins using 75 nickels, 60 dimes, and 31 quarters.
a. Explain why you cannot make identical stacks of coins without any coins left over.
b What is the greatest number of coin stacks you can make with the least number of coins left over? Explain how you found your answer
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Depends on what you mean by "stack" and "identical". Must a "stack" have more than one coin? Because if a single coin can constitute a "stack", and if "identical" means "having the same number of coins as another stack", the it is possible to separate the given set of coins into identical stacks. Specifically, 166 stacks of one coin each. On the other hand, if a stack must have at least two coins, then the smallest possible stack of quarters would be a stack consisting of all 31 quarters since 31 is prime.
This eliminates the possibility of identical stacks regardless of whether "identical" is based on number of coins or the value of the coins (i.e. a stack of five dimes is identical in value to a stack of two quarters). Since the only possible stack of quarters has 31 quarters with a value of $7.75, and considering that you do not have a multiple of 31 considering the total (135) of the dimes and the nickels or a multiple of $7.75 considering the total value of the dimes and nickels ($9.75).
The answer to your second question depends on which of the stated criteria, namely "greatest number of stacks" and "fewest leftover coins" has precedence (forcing 1 leftover gets you to one answer, and allowing 2 leftovers gets you to a different answer). You will have to nail down that definition as well as the other two definitions before I can help you further.
John
My calculator said it, I believe it, that settles it
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