Solve the problem.
-A chemist needs 9 liters of a 50% salt solution. All she has available is a 20% salt solution and a 70% salt solution. How much of each of the two solutions should she mix to obtain her desired solution?
A)4.5 L of 20%; 4.5 L of 70%
B)3.6 L of 20% ; 5.4 L of 70%
C)1.8 L of 20%; 7.2 L of 70%
D)2.7 L of 20%; 6.3 L of 70%

Question

Quizplus · Accepted Answer

We can use the method of setting up equations based on the amount of salt in each solution. Let x be the amount (in liters) of the 20% solution and y be the amount (in liters) of the 70% solution. Then we have:
0.20x + 0.70y = 0.50(9)         (equation based on the total amount and percentage of the desired solution)
x + y = 9                           (equation based on the total amount of the two solutions)
Solving these equations, we get x = 3.6 and y = 5.4, which means the chemist needs 3.6 liters of the 20% solution and 5.4 liters of the 70% solution. Therefore, the answer is B. Let x be the amount of 20% salt solution and y be the amount of 70% salt solution needed.
From the given information, we can form the following system of equations:
x + y = 9 (total volume needed)
0.2x + 0.7y = 0.5(9) (total salt concentration needed)
Solving these equations, we get x = 3.6 and y = 5.4, which means she needs 3.6 liters of 20% solution and 5.4 liters of 70% solution. Therefore, the answer is option B.

Solve the Problem. -A Chemist Needs 9 Liters of a 50% Salt Solution