The key to eat really cheap junk food is actually not buying ready-made food products in grocery stores and restaurants. Instead, the really cheap junk food is one prepared at home using cheap, raw ingredients. It is junk food, because it can be detrimental to your health because of the way it is prepared and how it is consumed.
Home-Made Big Mac
In order to make your own Big Mac at home, you will need enriched wheat flour, water, sugar, yeast, some kind of plant oil, salt, sesame seeds, milk and eggs (as dough conditioners), beef, salt, black pepper, lettuce, onions, cucumbers, vinegar, salt, and whole milk mozzarella cheese (because American cheese is really just mozzarella cheese with food coloring). You won't be able to replicate the McDonalds' recipe exactly, because some ingredients are not really for sale at retail stores independently, so instead of high-fructose corn syrup for the Big Mac sauce, you just have to substitute that with sugar. Also, given that a set of home-made hamburgers would probably be devoured within a few days, you don't have to add any more preservatives other than the salt, unless you want to leave the burgers in your refrigerator for months.
It is important to prepare the big batch of dough first. That is very time-consuming, so do that first. On the same day, you prepare pickled cucumbers. At the end of the first day, you are supposed to have cucumbers that are pickling and freshly baked hamburger buns. On the second day, you make the burger patties and assemble the burger parts together. I think it's best to make as many burgers as your ingredients allow, so that you can eat junk food as often as possible for a really cheap price.
Ready-made French fries at a fast food restaurant is not cost-effective. If you want cheap fries, then you have to make fries yourself. Buy a big bulk of Russet potatoes. The potatoes must be washed, peeled, and frenched. Then, they must be deep-fried in hot oil and cooled. You can use up the entire bag of potatoes to make a ton of French fries to complement your home-made Big Macs.
Sweetened Carbonated Water
To complete your burger-and-fries meal, you just have to have a machine that makes carbonated water. Add some sugar, and presto, you have home-made soda! On the other hand, if you are on a tight budget and can't afford a soda-making machine, you can just make fruit-infused water, sweetened with refined sugar. The fruit adds a fruity flavor, and the sugar adds a sweet flavor. If you are going to use fruit, then it may be best to wash the fruit first and peel the skin. If peeling the skin is not possible, then you may want to use organic fruits instead, because you are about to dunk the fruit into water. If you are going to use sugar, then it must be refined sugar, as that is more common and thus cheaper than unrefined sugar. Mix the sugar and water together at warm temperature on the stove, because warmer temperatures make things more soluble. Keep in mind that you don't want to add too much sugar. If you add too much sugar compared to the amount of water, then the sugar may precipitate out of the solution when the temperature falls to a drinkable level. Refined sugar and water can be collected in public places, so that may reduce the cost to just the fruit.