The answer is 31$ and 63 cents

Method : Lets assume Cent = z and $ = 100z    , no. of dollars =x and no.of cents = y

So,Initially he had 100zx + zy

Now after cashier’s mistake it becomes 100zy + zx

After spending 5 cents it becomes double

So now equation is 100zy + zx -5z = 200zx + 2zy

or      199x = 98y -5

Now,value of y cannot be greater than 100 (otherwise it becomes $)

so plotting values of y for 1 to 100,we get only 1 integer value for x  i.e. 31 for y = 63

Hence the answer 31$ and 63 cents

Enjoy!

Answer:  31.63 $

Let the amount in cents be x, and amount in dollars be y

1.  x>y (otherwise the second number would be smaller)

2. Amount of cents in second number is y, since y-5<x,  there must be 1 dollar carried forward when doubling.

3. Amount of dollars in second number is x, hence (x-1)/2=y (take away the 1 dollar carried forward then half)

4. y can also be expressed as y=2x-100+5 (double x and take away the 100 cents carried forward, then add the 5 cents)

5. Therefore (x-1)/2=2x-100+5

6. Solving the expression above gives x=63, and y=(x-1)/2=31

Hope all is clear:)