A metallurgist needs to make 124 lb of an alloy containing 5

A metallurgist needs to make 12.4 lb. of an alloy containing 50% gold. He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of each should he use?

Please solve and show all work. No handwritten work please.

Solution

A metallurgist needs to make 12.4 lb of an alloy containing 50% gold.
He is going to melt and combine one metal that is 60% gold with another metal that is 40% gold. How much of each should he use?
-------------------------------
Equation:
gold + gold = gold
0.60x + 0.40(12.4 - x) = 0.50*12.4
----
Multiply thru by 100 to get:
60x + 40*12.4 - 40x = 50*12.4
20x = 10*12.4
---
x = 6.2 lb (amt. of 60% alloy needed)
---
12.4-x = 6.2 lb (amt. of 40% alloy needed)