Three solutions contain a certain acid. The first contains 10% acid, the second 30%, and the third 50%. A chemist wishes to use all three solutions to obtain a 100-liter mixture containing 28% acid. If the chemist wants to use twice as much of the 50% solution as of the 30% solution, how many liters of each solution should be used?
A)49 of 10% , 17 of 30% , 34 of 50%
B)46 of 10% , 36 of 30% , 18 of 50%
C)45 of 10% , 19 of 30% , 36 of 50%
D)46 of 10% , 18 of 30% , 36 of 50%
E)43 of 10% , 19 of 30% , 38 of 50%

Question

Quizplus · Accepted Answer

The equations based on the problem are: x + y + z = 100 (total liters), 0.1x + 0.3y + 0.5z = 28 (acid concentration), and z = 2y (twice as much 50% solution as 30%). Solving these gives x = 46, y = 18, z = 36.

Three Solutions Contain a Certain Acid