A Level Chemistry EQ - NEED HELP!

Hi!! I'm really struggling on this question so would really appreciate some clarification on why the answer is the way it is. Here's the question:

The students collected a 20 cm3 sample of liquid and weighed it. The mass of the sample was 16 g.
The density of ethanol is 0.79 g cm−3 and that of water 1.00 g cm−3
.
Use these data to calculate the mass of ethanol in the sample collected.
You should assume that the volume of the sample is equal to the sum of the volumes of water and ethanol

And this is the mark scheme answer:
Volume of sample = volume of ethanol + volume of water
Let m = mass of ethanol
20 = m / 0.79 + (16–m) / 1.00
1.266m − m = 20 − 16

0.266m = 4 so m = 15 (g)

I really don't understand how they did it. Really appreciate the help!!!

Reply 1

TypicalNerd

Original post by MlightOr

(density in g cm^-3) = (mass in grams)/(volume in cm^3)

Therefore, (volume in cm^3) = (mass in grams)/(density in g cm^-3)

They’ve told you the total mass of the ethanol-water mixture is 16 grams, if you define the mass of ethanol in the mixture as x grams, then the mass of water is (16 - x) grams.

You can now use the rearranged density equation to find expressions for the volumes of water and ethanol in the mix:

V = m/ρ, so V(ethanol) = x/0.79 and V(water) = (16 - x)/1.00

The total volume of the mixture is 20 cm^3, so V(total) = 20 = V(ethanol) + V(water)

Using all the above information

20 = x/0.79 + (16 - x)/1.00

Trammel through the algebra and solve for x and you should get the answer as per the MS.