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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.

Respuesta :

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

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