A metallurgist has one alloy containing 46% copper and another containing 69% copper. How many pounds of each alloy must he use to make 43 pounds of a third alloy containing 60% copper?

Suppose x pounds of 0.46 copper and y pounds of 0.69 copper are used to make 43 pounds of 0.6 copper, thus

x+y=43

⇒x=43-y ... i

Also:

0.46x+0.69y=0.6*43

0.46x+0.69y=25.8 ... ii

substituting i in ii we get:

0.46 (43-y) + 0.69y=25.8

19.78-0.46y+0.69y=25.8

putting like terms together we obtain:

0.23y=6.02

y=26.174

hence:

x=16.826