Coins in Change under $1Date: 03/13/2001 at 12:45:51 From: LP FLOYD Subject: Coins It's been a long time since my last math class. Is there a formula or equation for determining the smallest number of coins a person could receive when given change less than $1.00? Ex: Item costs $.68. Customer gives cashier $1.00 and receives $.32 in change. What is the smallest number of coins the customer could receive for his change? I know this is easy to figure out by looking at it, but I'd like a standard formula or equation, if there is one, to use in a more complex problem. Date: 03/13/2001 at 16:32:47 From: Doctor Rob Subject: Re: Coins Thanks for writing to Ask Dr. Math. There is a cumbersome formula, and a rather easy algorithm. Here [[x]] means to round x down to the nearest whole number. Suppose for simplicity that half-dollars are excluded. Then the number of coins that make up N cents is given by [[N/25]] + [[(N - 25*[[N/25]])/10]] + [[N/5]] - 5*[[N/25]] - 2*[[(N - 25*[[N/25]])/10]] + N - 5*[[N/5]]. The first line is the number of quarters, the second the number of dimes, the third the number of nickels, and the fourth line the number of pennies. This can be simplified a little to N - 4*[[N/5]] - [[(N - 25*[[N/25]])/10]] - 4*[[N/25]]. If you allow fifty-cent pieces, the formula is N - 4*[[N/5]] - [[(N - 25*[[N/25]])/10]] - 4*[[N/25]] - [[N/50]]. If you also allow dollar coins, throw in another term on the end of -[[N/100]]. The algorithm is to give as many of the largest coins as possible, then the next largest coin, and so on. - Doctor Rob, The Math Forum http://mathforum.org/dr.math/ |
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