Question

A metallurgist needs to make 20 lb. of an alloy containing 45% gold. He is going to melt and combine one metal that is 57% gold with another metal that is 27% gold. How much of each should he use?

Answer 1

To create an alloy containing 45% gold, the metallurgist should use approximately 13.2 pounds of a 57% gold metal and 6.8 pounds of a 27% gold metal.

Step-by-step explanation:

To determine how much of each metal the metallurgist should use, we can set up an equation based on the amount of gold in each metal. Let's say the metallurgist uses x pounds of the 57% gold metal and (20 - x) pounds of the 27% gold metal. The equation would be:

0.57x + 0.27(20 - x) = 0.45(20)

Simplifying and solving for x, we find that the metallurgist should use approximately 13.2 pounds of the 57% gold metal and 6.8 pounds of the 27% gold metal.