word problem

Question

gold is 19 times as heavy as water and copper is 9 times as heavy as water in what ratio should these be mixed to get an alloy 15 times as heavy as water

 

 

please explain me

Answer 1

Let, density of water = d

Then, density of gold = 19d

and, density of copper = 9d

 

If we assume that we need x volume of gold and y volume of copper to get the density of the mixed alloy to be 15d

 

Then, we can apply the mass balance:

mass of gold + mass of copper = mass of alloy

 

Since mass = density*volume

 

19d*x + 9d*y = 15d*(x+y), since the volume of alloy = volume of gold + volume of copper

 

divide each side by d

19x + 9y = 15(x+y)

 

divide each side by y (since the ratio we want to find out would be x/y)

 

19(x/y) + 9 = 15(x/y) + 15

 

4(x/y) = 6

 

x/y = 3/2

 

So, the ratio of gold to copper is 3:2