Achef plans to mix 100% vinegar with italian dressing. the italian dressing contains 13% vinegar. the chef wants to make 150 milliliters of a mixture that contains 42% vinegar. how much vinegar and how much italian dressing should she use?

To determine the volume of both concentration of vinegar, we need to set up two equations since we have two unknowns. 

For the first equation, we do a mass balance:

mass of 100% vinegar + mass of 13% vinegar = mass of 42% vinegar

Assuming they have the same densities, then we can write this equation in terms of volume.

V(100%) + V(13%) = V(42%)
   we let x = V(100%)
             y = V(13%)

x + y = 150

For the second equation, we do a component balance:

1.00x + .13y = 150(.42)
x + .13y = 63

The two equations are
x + y = 150
x + .13y = 63

Solving for x and y,
x = 50
y = 100

Therefore, you need to mix 50 mL of the 100% vinegar and 100 mL of the 13% vinegar.