Math word problem!

[Marie]

Hi there!

I am quite stuck with this problem, and I wasn't too sure which category it belonged under. So here goes!

Let's say a robber has stolen money from a bank. It may have consisted of $50 and $100 bills or only $100 bills, or some combination of $5,$10,$20,$50 and $100 bills. How would I use a general method for figuring out whether or not a person (robber) could carry ANY amount of money, using ANY combination of bills.

I understand the situation - I am just unsure as to preparng a general method or formula.
Any suggestions would be much appreciated!

[stapel_eliz]

To my knowledge, there is no "formula" for this sort of exercise. You just have to work through the options and the logic until you determine the solution.

Have fun!

[LoveMath]

Marie,

The way you stated the problem, the possibilites are endless and, of course, nothing a person should ever consider. But, if you said that the person wanted $50,000 in 50's and 100's, even so, you can see that there are many, many ways that you can come up with the $50,000.

In order to come up with some equations, you would have to specify let's say that you want $50,000 in 50's and 100's and you wanted 600 bills in total. Then, if you set x = amt. of 50's and y = amt. of 100's, you'd have

x + y = 600 or y = 600-x and
$50x+$100y = $50,000

so using substitution, you have
50x + 100(600-x) = 50,000
50x + 60,000 -100x = 50,000
60,000-50x = 50,000
10,000 = 50x
200 = x
then since y = 600-x this gives 600-200 = 400

Answer: x = 200 = # of 50's
y = 400 = # of 100's