How much of each alloy should be mixed to attain the 100 grams of alloy with 16​% ​titanium?

Question

A metallurgist has an alloy with

1010​%

titanium and an alloy with

2020​%

titanium. He needs 100 grams of an alloy with

1616​%

titanium. How much of each alloy should be mixed to attain the 100 grams of alloy with

1616​%

​titanium?

Answer 1

Let x=mass of 10% titanium and y=mass of 20% titanium.

x+y=100 (total mass) so y=100-x

0.10x+0.20y=0.16*100=16 (quantity of titanium)

Substitute for y:

0.10x+0.20(100-x)=16

0.10x+20-0.20x=16

4=0.10x so x=40g and y=100-40=60g.

40g of 10% titanium mixed with 60g of 20% titanium will make 16% of alloy.