Let f and s denote the amounts of the first and second brands that the chef is going to use.
She wants to end up with 290 mL, so
f + s = 290
Each mL of the first brand contains 0.08 mL of vinegar, and each mL of the second contains 0.13 mL of vinegar. The final mixture should have a concentration of 12% vinegar, so that it contains 0.12 • 290 mL = 34.8 mL of vinegar, and
0.08f + 0.13s = 34.8
Solve for f and s :
f + s = 290 → s = 290 - f
0.08f + 0.13 (290 - f ) = 34.8
0.08f + 37.7 - 0.13f = 34.8
0.05f = 2.9
f = 58
s = 290 - 58
s = 232
