Question

A chef 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?

Answer 1

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.