Solve the problem.
-A chemist needs 180 milliliters of a 35% solution but has only 23% and 59% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.
A)60 ml of 23%; 120 ml of 59%
B)50 ml of 23%; 130 ml of 59%
C)130 ml of 23%; 50 ml of 59%
D)120 ml of 23%; 60 ml of 59%

Question

Quizplus · Accepted Answer

Let x be the amount of 23% solution needed and y be the amount of 59% solution needed.
Since the chemist needs a total of 180 milliliters and wants a 35% solution, we can set up the following system of equations:

x + y = 180        (equation 1)   - this is because he needs 180 ml of the final solution
0.23x + 0.59y = 0.35(180)     (equation 2)  - this is because the chemist wants a 35% solution

Simplifying equation 2, we get:
0.23x + 0.59y = 63

We can solve for either x or y in equation 1:
x = 180 - y

Substituting this into equation 2:
0.23(180-y) + 0.59y = 63

Simplifying and solving for y, we get:
y = 120

Substituting this value of y back into x = 180 - y, we get:
x = 60

Therefore, the chemist needs 60 ml of 23% solution and 120 ml of 59% solution to make 180 ml of 35% solution. Thus the answer is D. Let x be the amount of 23% solution needed and y be the amount of 59% solution needed. The total amount of solution needed is x+y=180 ml. Also, the amount of solute in the final solution can be expressed as 0.35(180)=63 ml. Setting up the system of equations:

x + y = 180
0.23x + 0.59y = 63

Solving for x and y, we get x=120 ml and y=60 ml, which corresponds to choice D.

Solve the Problem. -A Chemist Needs 180 Milliliters of a 35% Solution but 35