Chemistry: Algebra/Density Problem?

Question

It's been awhile and I don't know where to start with this problem =( help me gurus!

Determine how many grams of gold (Au) and how many grams of silver (Ag) are in a crown that has a mass of 2277g and a total volume of 165cm^3. Assuming the crown is made entirely of gold and silver. The densities of AG and Au are 10.5g/cm^3 and 19.3g/cm^3 respectively.

I really want to know how to do it instead of just the plain answer

Answer 1

let vol of Au = x cc
since the total vol = 165 cc
=> vol of silver = (165-x) cc
=> mass due to Au = vol of Au * density of Au = x * 19.3 g
=> mass due to Ag = vol of Ag * density of Ag = (165-x) * 10.5 g

=> total mass = x * 19.3 + (165-x) * 10.5 g
but given total mass = 2277 g

=>x * 19.3 + (165-x) * 10.5=2277
=> 19.3x - 10.5x + 1732.5 = 2277
=> 8.8x = 544.5
=> x = 544.5/8.8 = 61.875 cc
=>vol of Au = 61.875 cc

=> mass of Au = vol*density = 61.875*19.3 = 1194.1875 g.

=> mass of Ag = total mass - mass of Au=2277 - 1194.1875= 1082.8125 g.

Answer 2

You need to set up a system of two equations because you have two variables that are unknown.

The total mass is 2277g so you know that Mg (mass gold) + Ms (Mass silver = 2277 grams.

You also know that the total volume is 165 cm^3 and volume can be found by dividing the mass by the density so

Mg/19.3+Ms/10.5 = 165
Mg + Ms = 2277

Now you have to equations and two unknowns, you can solve by addition or substition, I will do addition.

Answer 3

Set up a linear system of equations.