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 10-liter mixture containing 24% 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)2.8 of 10% , 2.4 of 30% , 4.8 of 50%
B)5.8 of 10% , 2.8 of 30% , 1.4 of 50%
C)8.8 of 10% , 0.4 of 30% , 0.8 of 50%
D)4.8 of 10% , 2.4 of 30% , 2.8 of 50%
E)5.8 of 10% , 1.4 of 30% , 2.8 of 50%

Question

Quizplus · Accepted Answer

The equations based on the problem are: x + y + z = 10 (total volume), 0.1x + 0.3y + 0.5z = 2.4 (acid content), and z = 2y (twice as much 50% as 30%). Solving these gives x = 5.8, y = 1.4, z = 2.8.

Three Solutions Contain a Certain Acid