SOLUTION: A man received a check for a certain amount of money, but on cashing it the teller mistook the number of dollars for the number of cents and conversely. Not noticing this, the man
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Question 955163: A man received a check for a certain amount of money, but on cashing it the teller mistook the number of dollars for the number of cents and conversely. Not noticing this, the man spent 68 cents and discovered to his surprise that he had twice as much money as the check was originally drawn for. Determine the smallest amount of money for which the check could have been written for. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A man received a check for a certain amount of money, but on cashing it the teller mistook the number of dollars for the number of cents and conversely.
Not noticing this, the man spent 68 cents and discovered to his surprise that he had twice as much money as the check was originally drawn for.
Determine the smallest amount of money for which the check could have been written for.
:
I spent considerable time on this and found it can not out right as written unless I say he spent 58 cents instead of 68 cents.
:
let a = original number of dollars
let b = original number of cents
:
2(a + .01b) = b + .01a - .58
2a + .02b = b + .01a - .58
2a - .01a + .02b - b = -.58
1.99a - .98b = -.58
- .98b = - 1.99a - .58
multiply by -100
98b = 199a + 58
b =
the only integer solution to this is:
a = 46, then b = 94
The original check was $46.94
The teller gave him $94.46, he spent .58 so he had $93.88
This is twice $46.94
