This is hard question for a few reasons. First, does this budget mean the family gets $75 each week, or that they get $300 a month? There's a big difference in terms of cooking and meal planning. At $300 a month it would be challenging but not impossible, if you were willing to cut down big time on milk consumption (for older kids and teens) and have no pre-made snacks. With a $300 a month budget you can stock up on meat at .99 a pound when it goes on sale, freeze the excess, and buy condiments, oils, spices, and canned goods whenever they go on sale. Then, you could use the remainder to buy fresh produce and a few luxuries (chocolate, cheese) and roll over savings to the next month. For reference, $300 a month is my goal budget for two active adults in a very HCOL area in the US.
I think $75 a week would be significantly harder, because you would be forced to buy many items at full-price and you wouldn't be able to stock up on deals. Either way, it's an ok budget for an adult with two little kids, but an adult with two teens...doable, but not super easy.
The other major variables are time and ability. If this were a two parent family with one parent at home full-time, with the ability to bake bread, make sauces from scratch, make dried beans from scratch, etc...then $300 a month would be plenty! Of course, most people on such plans are working like crazy, do not have a stay at home spouse, and may or may not have serious cooking skills.