Pennies and RemaindersDate: 01/13/2003 at 18:18:47 From: Kelsey Subject: Pennies/word problems Arnie has between 300 and 400 pennies in his collection. When he divides them into groups of 4, 5, or 9 there is always one penny left over. How many pennies does Arnie's collection contain? Date: 01/14/2003 at 10:33:13 From: Doctor Kastner Subject: Re: Pennies/word problems Hi Kelsey - Let's think about an easier problem as a warmup. Suppose Arnie has between 40 and 50 pennies and he finds that if he divides them into groups of 3 or 7 he has one left over each time. How many pennies does Arnie have? The key here is to note that Arnie can ALMOST divide them into groups of 3 and 7. This suggests that we should look for a number that is a little more than a common multiple of 3 and 7. Well, 21 is a common multiple since both 3 and 7 go into 21 with no remainder. But we want a remainder of 1. So how about trying 22? That seems to work since 22 divided into groups of 7 gives 3 groups with one left over and 22 divided into groups of 3 gives 7 with one left over. Great! We are done! Oh...wait...he has between 40 and 50 pennies. Hmm...well, let's think about another common multiple of 3 and 7...how about 42? 3 goes into 42 evenly, and so does 7. But again, we want to have one left over each time, so let's add 1 to 42 which gives us 43. Does that work? Yes, 43 divided into groups of 3 gives 12 with 1 left over, and 43 divided into groups of 7 gives 6 with 1 left over. Now we are done. This is exactly the type of thing you need to do for your problem. I hope this helps. Write back if you're still stuck, or if you have other questions. - Doctor Kastner, The Math Forum http://mathforum.org/dr.math/ |
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