It is necessary to have a 40% antifreeze solution in the radiator of a certain car. The radiator now has 50 liters of 20% solution. How many liters of this should be drained and replaced with 100%
Antifreeze to get the desired strength?
A)20 liters
B)12.5 liters
C)25 liters
D)16.7 liters

Question

Quizplus · Accepted Answer

To achieve a 40% antifreeze solution in the radiator, we need to calculate the amount of pure antifreeze in the final mixture and set it equal to the amount of pure antifreeze we start with plus what we add. Initially, there are 50 liters of a 20% solution, so there are 50 * 0.20 = 10 liters of pure antifreeze. Let x be the amount of solution to drain and replace with pure antifreeze. After draining x liters of the 20% solution, we remove 0.20x liters of antifreeze. Adding x liters of 100% antifreeze adds x liters of antifreeze. The final volume remains 50 liters, and we want it to be 40% antifreeze, so we need 50 * 0.40 = 20 liters of pure antifreeze. Setting up the equation: 10 - 0.20x + x = 20. Solving for x gives x = 12.5 liters.

It Is Necessary to Have a 40% Antifreeze Solution in the Radiator