Ametallurgist has an alloy with 5% titanium and an alloy with 25% titanium. he needs 100 grams of an alloy with 13% titanium. how much of each alloy should be mixed to attain the 100 grams of alloy with 13% titanium

So... the alloy with 5% titanium is ...some  alloy :), so is a mixed metal and among its mix it has 5% of titanium, it has other metals, but only 5% is titanium.

that means that if the amount of it is say "x", then the amount of titanium in it will be 5% or (5/100) * x, or 0.05x.

now, the 25% titanium, is the same issue, if say a quantity of "y" will only have 25% of titanium, regardless of other metals, so in "y" there is 25% or (25/100) * y, or 0.25y.

so, we need a mixture that yields only a 13% alloy, or 13/100, and will be 100 grams, so the amount of titanium in it will then be (13/100) * 100 or 13.



how much of the 25% alloy will be needed?  well, y = 100 - x.