A 9 L solution that was 11% vinegar was mixed with a 10 L solution that was 69%vinegar. find the new concentration of vinegar

1st solution: 9L 11% Vinegar, 9, 11

2nd solution: 10L 69% Vinegar 10, 69

Total volume when mixed = 9 + 10 = 19

Using, law of mixtures:

Volume1 * Concentration 1 + Volume2 * Concentration2 = Total Volume * Final Concentration

Volume is in L, and Concentration is in %

9*11 + 10*69 = 19 * FC, Where FC = Final Concentration

99 + 690 = 19FC

789 = 19FC Divide both sides by 19

789/19 = FC

41.52 = FC

Therefore final concentration after mixing = 41.52%