## Monday, April 02, 2012

### Good Old Fashioned Banking

John needed some small bills because he was traveling. He went into a bank and gave the teller a \$100 bill. He told her, "I need some two-dollar bills, ten times as many one-dollar bills, and the rest in five-dollar bills. Assuming she didn't tell him to try his request online instead, how many of each did the teller give him?

1. 5 two-dollar bills
50 one-dollar bills
8 five-dollar bills

2. Anonymous is correct. It would be an interesting twist to the riddle, if you would change this sentence:

"I need some two-dollar bills, ten times as many one-dollar bills"

as follows:

"I need some one-dollar bills, ten times as many two-dollar bills"

This will make an interesting situation that there is no solution to the problem that includes \$2 and \$1 notes, but only 20 x \$5 notes. Here is the reasoning for this changed scenario:

GET TO 100d!!!

If we assume that John wants at least 1 x 1d bill, thus, (1) is not correct.
But since that is the only one that works out, John only gets 20 x 5d bills.
We assume that he gets whole bills only, thus, not 1.57 1d bills or something like that.

REASONING:

(2) - (5): remainder of 1d and 2d is not divisible by 5, so does not work out.

(6): Amount of 1d and 2d is over 100d, thus that does not work out.

We conclude that John gets only 20 x 5d bills and no 1d and 2d bills.

(1)
0 x 1d = 0
0 x 2d = 0
20 x 5d = 100

(2)
1 x 1d = 1
10 x 2d = 20
undefined x 5d = 79

(3)
2 x 1d = 2
20 x 2d = 40
undefined x 5d = 58

(4)
3 x 1d = 3
30 x 2d = 60
undefined x 5d = 37

(5)
4 x 1d = 4
40 x 2d = 80
undefined x 5d = 16

(6)
5 x 1d = 5
50 x 2d = 100
undefined x 5d = -5

Good puzzle, thanks!

Kobus

3. Got it too, though in a weird binary equation way. 2x+10x+5y=100
=>12x+5y=100
=>12x=100-5y
=>12x=5(20-y)
=>20-12/5x=y
=>20-2.4x=y
now, we know that y is a whole no. therefore, 2.4x must be a whole no. The nearest number that makes the expression whole is if we assume x=5.
Therefore, using this value in the first equation, we get
12*5+5y=100
=>y=8
And the rest follows..

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