Question

One alloy of brass is 70% copper and 30% zinc. Another alloy of brass is 40% copper and 60% zinc. How many grams of each of these alloys need to be melted and combined to obtain 300 grams of a brass alloy that is 60% copper and 40% zinc

Answer 1

Just concentrate on copper only.
let the amount of the 70:30 alloy used be x g
then the amount of the 40:60 alloy used is 300 - x
.7x + .4(300-x) = .6(300)
.7x + 120 - .4x = 180
.3x = 60
x = 200

so 200 g of the 70:30 alloy and
100 g of the 40:60 alloy

checking for the zinc:
.3(200) + .6(100) = 120
and .4(300) = 120, checks out!

Answer 2

By volume, one alloy is 60% copper, 30% zinc and 10% nickel. A second alloy is 50% copper, 30% zinc and 20% nickel. The third alloy is 30% copper and 70% nickel. How much of each alloy is needed to make 100 cm^3 of a new alloy that is 40% copper, 15% zinc and 45% nickel?