Math Problem♥?

Question

A woman went into a bank to cash an insurance refund check. By mistake the teller gave her dollars for cents and cents for dollars. She put the money in her purse but accidentally dropped a nickel on the floor. When she got home, she found that she had exactly twice the amount of the check she had cashed. She didn't have any money in her wallet before going to the bank. What was the exact amount of that check?

And no this isn't for school because we go back the 21st I just found it and thought you would enjoy doing it :)

Answer 1

Let d = the dollar of the check
c = the cents part of the check

Thus,
[100d + c] cents = actual check amount
[100c + d] cents = wrong amount given by the bank
[100c + d - 5] cents = money in wallet when she got home

Since her money in wallet when she got home is twice the actual check amount,
(100c + d - 5) cents = 2(100d + c) cents

remove the cents
100c + d - 5 = 2(100d + c)

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

combine like terms
100c - 2c - 5 = 200d - d

simplify
199d = 98c - 5

thus,
d = (98c - 5)/199

The dollars and the cents must be whole numbers, and 2 < c < 100, so try to find values for c that will make d a whole number (i.e., 98c - 5 is divisible by 199)

If we let c = 63, d = 31.

Therefore the actual check amount is $31.63

^_^

Answer 2

"Let's say that the check was for x dollars and y cents. The check is worth:

(100x + y) cents

The bank makes a mistake, and gives you y dollars and x cents, or:

(100y + x) cents

After dropping a nickel (some real sport you are,giving away a whole nickel after the bank made an error in your favor), you have:

(100y + x - 5) cents

Since this is twice the amount the check was worth:

100y + x - 5 = 2(100x + y)

100y + x - 5 = 200x + 2y

98y - 5 = 199x

98y = 199x + 5

y = (199x + 5)/98

Since x and y must be integers, we should check to see what integral value(s) for x will make y an integer. x must be odd, since 199x must be odd in order for the sum (199x + 5) to be even, a prerequisite to being divisible by 98.

Since 199 = 3 mod 98, and we need to find an odd x such that:

199x = 93 mod 98.

It seems as thought x could be 31, which would make y 63.

If the bank gave you $63.31 for a $31.63 check, you could give away a nickel and the $63.26 you had left would be twice the value of the check."

Answer 3

The amount must have been $31.63. She received $63.31. After she dropped a nickel there would remain the sum of $63.26, which is twice the amount of the check.

Answer 4

My first approach was to consider the original amount as (ab.cd $), therefore the equation would become
(cd.ab) - 0.05 = 2 (ab.cd)....somehow the logic is right but something's fishy....reading the answer posted now.

That was an interesting math problem...didn't think to convert everything in cents in the first place though. lol

Answer 5

let the check be for 'x' dollars and 'y' cents
100y+x-5=2(100x+y)
98y-199x=5

Answer 6

2x2=4

Answer 7

- five cent i guess.