Tuesday, February 09, 2010
Check, Please
A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check?
Subscribe to:
Post Comments (Atom)
$18.56
ReplyDeletewe ARE extremely rusty in our
ReplyDeletealgebraic skills. :-)
we spent an inordinate (pun!)
amount of time juggling
x's, y', a' & b's with nothing
to show for it except a proper humbling.
{our guess is that it was overdue}
we were able, however,
to confirm Andy's answer through other means.
it appears that $18.56 is correct. kudos!
and thanks for the twister
..
.ero
Let x be the number of dollars in the check, and y be the number of cents.
ReplyDeleteThen 100y + x − 50 = 3(100x + y).
Therefore 97y − 299x = 50.
Keep in mind that x and y have to be between 0 and 100
It can be shown that all integer solutions of 97y − 299x = 50 are of the form y = 1850 + 299k, x = 600 + 97k, where k is any integer. (I'm not going to show this... too much writing!)
In this case, because x and y must be between 0 and 99, we choose k = −6.
This gives y = 56, x = 18.
So the check was for $18.56.
In case anyone cares to know, the way I found this one was sort of a brute force method. I got the equation that Mike mentioned, and solved for x:
ReplyDeletex = (97y - 50)/299
Then I used a quick spreadsheet to find x for all possible values of y (00...99), and found that x=18, y=56 was the only one that came out to integer values, so that was my answer.
Not sure if the spreadsheet is considered cheating though :)