How much would a 10k gold female class ring be worth if you resold it to a pawn shop? What would a be a reasonable price to resell it?

You can't expect to get an answer to this unless you provide additional information. Is is solid gold or plated? How much does it weigh? Are there stones that add to the weight? Even knowing all of that, you would be offered anywhere from 20 to 70 percent of the gold value, depending on how unscrupulous your buyer is. Find a kitchen scale and figure out the weight of your item in grams, and any website with a gold calculator will be able to show you how to convert your weight into troy ounces and figure out approximately what it is worth based on the current price of gold.

Cheaper ( 10K) type rings at pawn shops, rough general rule if you get 20 or 30 bucks for one you will be lucky.

Generally speaking class rings are 10K, sometimes 14K. They are clearly stamped inside the ring. If it is not stamped chances are about 99.9% it is not gold. To find out what it is worth go to several places that advertise buying gold. Absolutely do not sell to the first price you get, shop several different stores. Guessing at the price would only be just that, a guess.
If you really want a formula, here goes:
(spot price of gold) X karat / 24 (kt)= 100% of value of gold in troy ounces. Or you can multiply:
.417 X spot gold for 10K
.583 X spot gold for 14k
.750 X spot gold for 18K
31.1 grams = 20 dwts (pennyweights) = 1 troy ounce.
Remember one ounce of hamburger is one ounce avoirdupois = 28.35 grams (troy ounce is about 10% heavier) IF your ring weighs one ounce on your kitchen scale it is about .9 ounces in troy weight.
A top notch gold buyer will pay between 70% and 80% of this number, I have heard of a pawn shop that pays less than 10% of that number.
By the way don't forget to subtract for the weight of the gemstone, 99% of them are worthless.