Question

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?

Answer 1

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