Dan went into the bank to cash a check. In handling the money, the cashier, by mistake, gave him dollars for?

Question

cents and cents for dollars. He pocketed the money without examining it, and spent a nickle on his way home. He than found out that he possessed exaclty twice the money of the check. He had no money in his pocket before going to the bank. What was the exact amount of the check?

Answer 1

Let d be the amount of dollars the check was for and c be the amount of cents. Thus, the check would have been for a total of 100d + c cents. However, he received 100c+d cents, so we have:

100c+d-5=2(100d+c)
solving for c:
100c+d-5=200d+2c
98c=199d+5
c=(199d+5)/98

Now, since c is a whole number, we have that 199d+5 must be a multiple of 98 - i.e. 199d+5≡0 mod 98. This means that 3d≡93 mod 98. Using the extended euclidean algorithm (http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm ):

gcd x y
98
3 -1 33
2 1 -1
1 0 1

Thus -98+33*3≡1 mod 98, and 33*3≡1 mod 98

so we return to 3d≡93 mod 98
multiplying both sides by 33:
d=31 mod 98

Thus d is 31 (plus or minus an exact multiple of 98, but since d has to be a positive two digit number, it clearly is 31). Then from our original equation:

c=(199d+5)/98
c=6174/98
c=63

So the check was for $31.63.

Answer 2

So if the check was worth d dollars and c cents, or 100d + c cents, he actually got c dollars and d cents, later spending 5 cents, ending up with c dollars and (d-5) cents or 100c + d - 5 cents.

But 2(100d + c) = 100c + d - 5

200d + 2c = 100c + d - 5

199d = 98c - 5

d = (98c - 5)/199

So 98c - 5 is a multiple of 199, since d is a whole number. This happens if c = 63.

98X63 - 5 = 6169 / 199 = 31

So the check was for $31.63. He received $63.31, spent 5 cents, and had $63.26.

Answer 3

What are you supposed to do with the money? If you received an unsolicited cashier's check in the mail, their is a 99.99% chance that the check is fake anyway and will bounce. If you were supposed to cash it and send some of the money out via Western Union, there is a 100% chance that the check is fake and will bounce.

Answer 4

I give up! I have everyone here in the office working on it....

haha

I can't wait to see the answer :)

Answer 5

What did he buy for a nickle!!

Answer 6

Is there really an answer to that?? lol

Answer 7

i really can't say!!!!