Question

A metallurgist has an alloy with 16​% titanium and an alloy with 30​% titanium. He needs 100 grams of an alloy with 23​% titanium. How much of each alloy should be mixed to attain the 100 grams of alloy with 23​% ​titanium?

nothing grams of the alloy with 16​% of titanium are needed.

Answer 1

Let x = amount of 16% alloy, and y = amount of 30% alloy he should use.

Mixing the alloys will result in a compound weighing x + y = 100 grams.

For each gram of the 16% alloy used, 0.16 gram of titanium is contributed; similarly, for each gram of the 30% alloy used, there's a contribution of 0.3 gram. He wants to end up with an alloy of 23% titanium, or 23 grams (23% of 100), so that 0.16x + 0.3y = 23.

Solve the system:

`x+y=100\implies y=100-x`

`0.16x+0.3y=23\implies 0.16x+0.3(100-x)=23\implies7=0.14x`

`\implies\boxed{x=50}\implies\boxed{y=50}`