Alloy Question

Question

An alloy is made from a mixture of gold and silver. The density of gold is 19.3 g/cm^3. The density of silver is 10.5g/cm^3. A ring is made from the alloy. The mass of the ring is 10g and its volume is 0.6cm^3 Use algebra to show that about 70% of the volume of the ring is gold.

Answer 1

Density = Mass / Volume or   D = M/V

 

Let
X = mass of the Gold
Y = mass of the Silver

Vg = volume of Gold
Vs = Volume of Silver

19.3 g/cm^3 = X/Vg --> 19.3*Vg = X   <--- mass of the gold in terms of it's density and volume

10.5 g/cm^3 = Y/Vs --> 10.5g * Vs = Y  <--- mass of the silver in terms of it's density and volume

X + Y = 10   <--- total mass is 10 grams


19.3*Vg + 10.5* Vs = 10 g    <--- substitutes the two equations for each mass of gold and silver respectively;

                                                       label this equation ALPHA

 

Total volume is 0.6, so

Vg + Vs = 0.6 cm^3 --> Vg = 0.6 - Vs  <--- label this equation BETA

 

Substitutes equation BETA into equation ALPHA

19.3*(0.6 - Vs) + 10.5*Vs = 10

11.58 - 19.6* Vs + 10.6 * Vs = 10

-9 Vs = -1.58

Vs = .175555...         -->                 Vg = 0.6 - .175555....     =    0.424444....

So out of a total volume of 0.6, the gold is 0.4244444

 

Therefore, the
Percent Volume of Gold is 0.4244444.../0.6 = .70740740740.....

which is about 70%