Spoiler!

 

Over the long haul, then, you'd get N sets of 0 cents, 1 cent, 2 cents, and so on up to 99 cents. So let's consider one of each. How many of each coin would you end up with?

Easy first: let's do quarters. 25-49 cents each gets you one. 50-74 each gets you two. 75-99 each gets you three. That's (1+2+3)*25, or 150 quarters.

Dimes next. 10-19 gets you one. 20-24, two. (You'd get a quarter instead for 25 and up.) 35-44, one. 45-49, two. 60-69, 85-94, one. 70-74, 95-99, two. So that's 4*(10+5*2), or 80 dimes.

Nickels. One for 5-9, 15-19, and that same pattern for +25, +50, +75, so it's 4*10 or 40 nickels. You'll never get two at a time, since a dime (at least) will do.

Pennies. Let's cut to the chase: 1,2,3, and 4 cents gets 10 pennies in all, and that pattern happens 20 times, so that's 200 pennies.

Let's double-check. 200 pennies, 40 nickels, 80 dimes, 150 quarters. That's 200*1 + 40*5 + 80*10 + 150*25 cents = 200+200+800+3750 = 4950 cents, which is the sum of all numbers from 0 to 99, so it checks.

15/8/4/20 would be the ratio then, IF coin rolls all hold the same number of coins, but they don't. Quarter rolls hold 40 coins, dime rolls hold 50, nickel rolls 40, penny rolls 50. So you need 5/4 as many quarter and nickel rolls. The final ratio is 75/32/20/80. Seems like a lot of quarters and pennies, except for the assumption that you'll tend to get them much more often than nickels and dimes as change.

 

hehe. sorry.

I figured it's almost the end of the day, so what the heck?