When the manager gave back the $5 it turned the bill from being $75 to being $70. $70 divided by the 3 people who paid equals 23.33333 (etc.). Each diner paid 23.33 (after rounding). $23.33 times 3 equals $69.99, leaving 1 cent toward the food and the $2.00 that the waiter got. $2.01 divided by 3 equals 67 cents (paid by each of the diners). 23.33 plus .67 comes to the $24 that each paid.
(Now, I'm guessing I may learn that this was a trick question and all that figuring was for naught..... )
Any way you look at it, the waiter got stiffed on the tip.
But yes, the key is realizing that the total bill is $70 after the manager's discount-- but the waiter, because he didn't have a convenient way to divide the $5 refund by three people, only gave them $3 of the discount -- making their total bill $72. The restaurant got $70-- waiter got $2. I think.
Okay, just heard this on a TV programme/documentary, but sadly missed the crucial solution. It is now bugging me no end, I just can't explain it, so I need someone, anyone in fact, to explain to me how this works. Here...