Calculate Fair Prize Values for Four Prize Winners.

Seems simple, but I'm having trouble determining this.

I'm trying to run a scenario analysis on the prize $ winnings for four winners, depending on the number of participants.

Each participant buys in for $35, but the thing is that the 4th place winner must always win back the $35 they used to participate, while the other three prize winners win more $ depending on their placement.

So essentially I need help coming up with a formula that calculates fair winnings for the 1st, 2nd, and 3rd place prize winners, and each of those must obviously be higher than $35 while also being higher than the subsequent winner; the combination of all the prize values for the four tiers must equal the total pot (# of participants x $35).

I've attached a simple excel spreadsheet that may better explain what I need help with.

Thanks!

Update: Figured this out. No need for a reply.

Please describe your solution for others seeking to solve a similar problem. Thanks.

Total price to divide for nr 1-3

Buy in Price x(# of Participants -1)

Nr 1 50%
Nr 2 30%
Nr 3 20%