How to cook for a big group
If you have time, make the dish at your normal size and measure everything you put in. This will allow you to get a recipe with proportions that you can use for your full party. Measuring weight is best if you have a scale, but volume should still be significantly better than guessing. 

Say you make your dish and it uses


w grams potatoes 
x grams sweet potatoes
y grams carrots 
z grams onions


If this feeds 4 normal people, then for 60 people you need


(60 / 4) * w grams potatoes 
(60 / 4) * x grams sweet potatoes
(60 / 4) * y grams carrots 
(60 / 4) * z grams onions