A sample of vinaigrette salad dressing has a total mass of 188 g, a total volume of 196 cm3, and consists only of oil (density = 0.899 g/cm3) and vinegar (density = 1.056 g/cm3). What is the volume of each component in this mixture? Assume that the volumes are additive.

Answer;

111 cm³ and 85 cm³

Explanation;

Equation 1: 0.885x + 1.056y = 188

Equation 2: x + y = 196

let x and y represent volume. x is volume for oil and y is volume for vinegar. Volume multiplied by density would leave you with grams, so since the salad dressing has total mass of 188, we'll set the 1st equation to that. x + y = total volume.

Solve the system of equations.

Multiply 2nd equation by - 0.885

-0.885 (x + y = 196) - --> - 0.885x - 0.885y = - 173.46

Add both equations.

0.885x + 1.056y = 188

-0.885x - 0.885y = - 173.46

X variable cancels out, leaving you with:

0.171y = 14.54

y = 85cc

Plug y back into 1st equation or 2nd.

0.885x + 1.056 (85) = 188

0.885x = 98.24

x = 111cc

Verify: Plug x and y into 2nd equation

111cc + 85cc = 196cc check

So, x = 111 and y = 85