Tricky math question....?

Question

This one took me a while but I finally figured it out...

A guy goes to a bank to cash a check. The teller makes a mistake and switches the dollars and change around (example if the check is $50.12, he gets $12.50 instead). He then spends five cents on a stick of gum and goes home. He counts his money and now has exactly double the amount of what the check should have been. How much was the original amount on the check?

The example is just that, an example. It has nothing to do with the question. And 70.35 is wrong.

ROGUE_OF_SHADOWS
Can you please explain how you do this part of this question:
199x + 5 is congruent to 0 (mod 98)
199 is congruent to 3 (mod 98)
Therefore, 3x + 5 is congruent to 0 (mod 98)
Mainly, what does (mod 98) mean? And how you came up with the number 3?

Answer 1

$31.63

Answer 2

The check value should be A+0.01B
The mistaken value is B+0.01A,
he spent five cents , and the money double so
2(A+0.01B)=(B+0.01A)-0.05
2A+0.02B=B+0.01A-0.05
1.99A=0.98B-0.05
1.99A=0.98B-0.05

Now I suppose that the value of A and B should be a whole number, so :
98B-5=199n, where n is a whole number.
By trial and error I found that B=63 and A=31.

So the check value is $31.63, mistaken for $63.31, then he bought $0.05 gum, so his money is $63.26, which is exactly twice the amount of $31.63

The original check value is $31.63

Answer 3

(example if the check is $50.12, he gets $12.50 instead).

Is that part of the question or did you just throw it in there? Im fixated on that part.

Answer 4

What a question hmmm 5 dollars

Answer 5

7035