Total volume of the sample = [tex]196cm^{3}[/tex]
Let the volume of oil be x
Volume of vinegar be y
x + y = [tex]196cm^{3}[/tex]------------------Equation-1
Density of oil = 0.909 [tex]\frac{g}{cm^{3} }[/tex]
Density of vinegar = 1.056 [tex]\frac{g}{cm^{3} }[/tex]
Mass of oil = x * 0.909 [tex]\frac{g}{cm^{3} }[/tex]=0.909x
Mass of vinegar = y * 1.056 [tex]\frac{g}{cm^{3} }[/tex]=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 [tex]cm^{3}[/tex]
Finding out the value of x :
x + y = 196
x + 66.9 = 196
x = 129.1 [tex]cm^{3}[/tex]
Therefore, the volume of oil = 129.1 [tex]cm^{3}[/tex] and volume of vinegar = 66.9 [tex]cm^{3}[/tex]
