A silversmith has two alloys, one containing 60% silver and the other 20% silver. How much of each should be melted and combined to obtain 600 grams of an alloy containing 48% silver?

Question

A silversmith has two alloys, one containing 60% silver and the other 20% silver. How much of each should be melted and combined to obtain 600 grams of an alloy containing 48% silver?

20% silver alloy	g
60% silver alloy	g

Answer 1

Use a weight average. Let x = amount of 60% material and 600-x = amount of 20% material.

Then

{ 60x + 20(600-x) }/600 = 48

You find that

x = 420 and 600 - x = 180