It appears that you do have enough information to calculate what you want, even without the final cost.
For example, say you have a recipe (chocolate chip cookies) that's initially 33% flour and flour is 1$/lb, that means you spend 0.33$/lb on flour per chocolate chip cookie (33% = 0.33, 1$/lb * 0.33 = 0.33$/lb)
Then all of a sudden, due to supply chain issues or something similar, the price of flour rises to 1.10$/lb, the same calculation can be applied with the new price (1.10$/lb * 0.33 = 0.36$/lb). This is the new cost of flour per pound of chocolate chip cookies produced.
Finally, to calculate the increase in price, you subtract the old price from the new one (0.36$/lb - 0.33$/lb = 0.03$/lb). This is how much your final price has increased.
In general, the formula for the price increase would be x = (N-n)*p, where x is the price increase, N is the new price, n is the original price, and p is the percentage of ingredient used in the recipe (expressed as a decimal).
and therefore the new price would be C = (c + x), where C is the new price, c is the original price, and x is the price increase.
Alternatively, you can combine the two formulas above to give C = c + (N-n)*p