I mix syrup by the sugar bag, and by far the easiest way to get the ratio right without doing any math and without having to remember a recipe is to look at the weight of the bag in kilograms. A liter of water weighs one kilogram, so just add that number of liters of water for 1:1 or half that number of liters for 2:1. Most pitchers are marked in liters so this is super easy even if you don't understand the metric system at all.
This method has zero math to do and I am not trying to convert gallons to pounds.
For example, if you look at the bottom of a 10 lb bag of sugar, next to the Net.Wt. 10 LBS you'll see 4.5 Kg. That means that to make 1:1 you will add 4—1/2 liters of water. To mix 2:1 you will add 2—1/4 liters of water.
I assume one quart (or liter) of water weighs about 2 pounds. I mix about 5 quarts of water with 10 lbs of sugar to make 1:1 syrup, and about 2.5 to make 2:1. It is not an exact science and as long as you are close you are fine.
5 gallon pail, mark it off in gallon increments. I never add more than 4 gallons in a bucket because of splash factor. Fill pail to desired amount with sugar up to one of the lines you marked off. Example up to 2 gallon line. Top off with hot water to that line. You have 2:1.