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.

As a project for math class, two students devised a game in which 3 black marbles and 2 red marbles are put into a bag. first the players must decide who is playing black marbles and who is playing red marbles. then each player takes a turn at drawing a marble, noting the color, replacing the marble in the bag, and then drawing a second marble and noting the color before returning it to the bag. the point scheme for the game is detailed in the table below. point values for marble game black marble points red marble points both black: +2 points both red: +4 points different colors: –1 point different colors: –1 point both red: 0 points both black: 0 points