Question

A sample of vinaigrette salad dressing has a total mass of 188 g, and a total volume of 196 cm^3 and consists of only oil (.909g/cm^3) and vinegar (1.056 g/cm^3) what is the volume of each component of the mixture

Answer 1

Total volume of the sample =
`196cm^(3)`

Let the volume of oil be x

Volume of vinegar be y

x + y =
`196cm^(3)`------------------Equation-1

Density of oil = 0.909
`(g)/(cm^(3) )`

Density of vinegar = 1.056
`(g)/(cm^(3) )`

Mass of oil = x * 0.909
`(g)/(cm^(3) )`=0.909x

Mass of vinegar = y * 1.056
`(g)/(cm^(3) )`=1.056y

Total mass of sample = 188 g

0.909x + 1.056y=188 ------------------ Equation -2

Using the equation x + y = 196 ==> x = 196 - y in equation-2 we get,

0.909x + 1.056y=188

0.909(196 - y) + 1.056y=188

178.196 - 0.909 y + 1.056 y = 188

178.196 + 0.147 y = 188

0.147 y = 9.831

y = 66.9
`cm^(3)`

Finding out the value of x :

x + y = 196

x + 66.9 = 196

x = 129.1
`cm^(3)`

Therefore, the volume of oil = 129.1
`cm^(3)` and volume of vinegar = 66.9
`cm^(3)`