Solve the problem.
-Dmitri needs 6 liters of a 46% solution of sulfuric acid for a research project in molecular biology. He has two supplies of sulfuric acid solution: one is an unlimited supply of the 54% solution and the other an unlimited
Supply of the 30% solution. How many liters of each solution should Dmitri use?
A)54% solution: 4.5 liters; 30% solution: 1.5 liters
B)54% solution: 4 liters; 30% solution: 2 liters
C)54% solution: 2 liters; 30% solution: 4 liters
D)54% solution: 3.5 liters; 30% solution: 2.5 liters

Question

Quizplus · Accepted Answer

Let x be the amount (in liters) of the 54% solution needed and y be the amount (in liters) of the 30% solution needed. Then we have the system of equations:

x + y = 6 (total solution needed)
0.54x + 0.30y = 0.46(6) (amount of acid needed)

Simplifying the second equation, we get:

0.54x + 0.30y = 2.76

Multiplying both sides of the first equation by 0.54 and subtracting from the above equation, we eliminate x and get:

0.20y = 0.48

Therefore, y = 2.4. Substituting into the first equation, we get x = 3.6. Therefore, Dmitri needs 4 liters of the 54% solution and 2 liters of the 30% solution. So, the answer is B). Let x be the amount of the 54% solution and y be the amount of the 30% solution. We have the following system of equations:
x + y = 6 (total volume is 6 liters)
0.54x + 0.30y = 0.46(6) (total amount of sulfuric acid should be 46% of the total volume)
Solving the system, we get x = 4 and y = 2, which means Dmitri should use 4 liters of the 54% solution and 2 liters of the 30% solution. Therefore, the best choice is B.

Solve the Problem. -Dmitri Needs 6 Liters of a 46% Solution of Sulfuric