word problem doubt

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 alloy 15 times as heavy as water

Answer 1

It should read "denser" not heavier. 

G = 19 * W
C = 9 * W

A * G + B * C = 15 * W * (A + B)
A * (19W) + B * (9W) = 15W * (A + B)
19A + 9B = 15 * (A + B)
19A + 9B = 15A + 15B
4A = 6B
A = (3/2) * B

So, for each part of Gold, there needs to be 1.5 parts Copper making the gold to copper ratio 3:2

 

Answer 2

a = amount of gold

b = amount of copper

 

Weight of gold    = 19a

Weight of copper =  9b

 

So 19a + 9b = 15(a + b).  Distribute, combine like terms:

 

4a = 6b, or 2a = 3b, so a/b = 3/2 

 

So gold : copper = 3 : 2