I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
Pages
▼
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?
5 two-dollar bills
ReplyDelete50 one-dollar bills
8 five-dollar bills
Anonymous is correct. It would be an interesting twist to the riddle, if you would change this sentence:
ReplyDelete"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
Got it too, though in a weird binary equation way. 2x+10x+5y=100
ReplyDelete=>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..