Ametallurgist 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.

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:

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