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First part of the question

A bank was robbed this morning. A lone robber carried the loot away in a big leather bag. The manager of the bank said that the money stolen consisted of small bills: \$5, \$10, and \$20. Throughout the day, some news stations have reported that the robber stole approximately \$1,000,000 in small bills, but Becky, a senior investigative reporter at Channel 10 News, thinks this is more money than one person could carry.

Becky wants to know how hard it would be for one person to carry \$1,000,000 in small bills. Investigate this question to determine if it is possible.

Second part of the question

Becky knows that she will have to investigate and report on other bank robberies in the future. In other robberies, the money stolen might not consist only of small bills. For example, it might consist \$50 and \$100 bills, or only \$100 bills, or some combination of \$5, \$10, \$20, \$50 and \$100 bills. Becky would like to be able to prepare quickly for her news reports without having to ask you for help each time a bank is robbed.

Describe a general method for her to use in preparing for future bank robbery reports (using appropriate algebraic expressions) for figuring out whether or not a person could carry any amount of money, using any combination of bills.

I know that I should start with the second part of the question in order to work out the first, but I am unsure of which direction to take. Any suggestions would be much appreciated, thank you!

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How much does a bill weigh? Or how much does a pack of say 100 bills weigh? –  mixedmath Sep 10 '12 at 3:51
    
Any denomination bill should weigh 1 gram. –  Mckenzie Sep 10 '12 at 3:53
    
How much weight can a person carry? –  mixedmath Sep 10 '12 at 3:54

1 Answer 1

A bill (whether it's a 1, 5, 100, whatever) weighs about 1 gram. (you can google this, that's how I got this figure, and probably how you're expected to proceed.)

So, if the robbers stole a bag full of bills, totaling a million dollars, and all the bills were 5's, 10's and 20's, what is the most that bag could weigh? Obviously the bag would be heavier if it were full of 200,000 \$5 bills vs. 100,000 \$10 bills, right?

So, in this heaviest-case, the bag weighs 200,000 grams. Is that a reasonable amount to carry? That would be 200 kg, or about 440 lbs.

To generalize this, go through the same thought process - based on the amount of money stolen, and the types of bills stolen (really, you only care about the smallest denomination stolen, right?), how heavy could that bag be?

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Thank you! That does make perfect sense - however, I know that it can be done. I just don't know how to get there. For the first part of the question, I don't mean carrying ONLY $5 bills or carrying ONLY $10 bills etc, I mean carrying any combination of the 3 (5, 10 and 20). I am unsure as to how to come up with a general method for showing and justifying this. –  Mckenzie Sep 10 '12 at 4:04
    
So I suppose you wouldn't shove money in a bag - you'd want to occupy space so therefore you would tightly stack the bills? –  Mckenzie Sep 10 '12 at 4:07
    
Yeah, I think this problem assumes the volume of the bills isn't a problem, just the weight. To answer your other question, think about how light the bag could possibly be - in the first case, this is if all bills are \$20's, and the bag weighs 50 kg. So no matter what mix of bills you have, the bag weighs somewhere between 50 and 200 kg. So, you might reasonably answer "It is possible if it was mostly \$20's (i.e., a weight close to 50kg), but not possible if it was mostly \$5's (200kg is too much for one person to carry around)". –  BaronVT Sep 10 '12 at 4:13
    
So I am assuming from the questio that they want a formula (general method) or an equation to kind of back that up. –  Mckenzie Sep 10 '12 at 4:16
    
Yeah, the question is stated a little vaguely, but I think they just want you to describe a general method to get a range of weight, and then say whether or not it would be realistic to carry (I think about 50kg is a reasonable max weight to expect the robber can carry). –  BaronVT Sep 10 '12 at 4:19

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