Let [tex]x[/tex] be the amount (mL) of the pure vinegar the chef will use, and [tex]y[/tex] the amount of dressing. She wants to end up with a 310 mL mixture, so
[tex]x+y=310[/tex]
For each mL used of the dressing, 0.07 mL is vinegar, and the chef wants to end up with a 19% vinegar mixture, so
[tex]x+0.07y=0.19(x+y)=58.9[/tex]
Now
[tex]x+y=310\implies y=310-x[/tex]
[tex]\implies x+0.07(310-x)=58.9[/tex]
[tex]\implies0.93x+21.7=58.9[/tex]
[tex]\implies0.93x=37.2[/tex]
[tex]\implies x=40[/tex]
[tex]\implies y=270[/tex]
