A chemist needs 10 liters of a 25% acid solution.The solution is to be mixed from three solutions whose concentrations are 10%,20%,and 50%.How many liters of each solution will satisfy each condition? Use 2 liters of the 50% solution.
A)7 L of 10%,7 L of 20%,2 L of 50%
B)1 L of 10%,2 L of 20%,7 L of 50%
C)1 L of 10%,7 L of 20%,1 L of 50%
D)1 L of 10%,7 L of 20%,2 L of 50%
E)7 L of 10%,1 L of 20%,2 L of 50%

Question

A chemist needs 10 liters of a 25% acid solution.The solution is to be mixed from three solutions whose concentrations are 10%,20%,and 50%.How many liters of each solution will satisfy each condition? Use 2 liters of the 50% solution. ​
A)7 L of 10%,7 L of 20%,2 L of 50%
B)1 L of 10%,2 L of 20%,7 L of 50%
C)1 L of 10%,7 L of 20%,1 L of 50%
D)1 L of 10%,7 L of 20%,2 L of 50%
E)7 L of 10%,1 L of 20%,2 L of 50%

Quizplus · Accepted Answer

Let x be the amount of 10% solution and y be the amount of 20% solution.
Then we have the following equations:
x + y + 2 = 10 (total volume)
0.1x + 0.2y + 1(2) = 0.25(10) (total amount of acid)
Simplifying the equations, we get:
x + y = 8
0.1x + 0.2y + 2 = 2.5
0.1x + 0.2y = 0.5
Multiplying the second equation by 10, we get:
x + 2y = 6
Solving the system of equations, we get:
x = 1, y = 7
Therefore, we need 1 liter of 10% solution, 7 liters of 20% solution, and 2 liters of 50% solution. The answer is D.

A Chemist Needs 10 Liters of a 25% Acid Solution