mixture problem

Question

The cooling system of a car has a capacity of 15 liters. The system is currently filled with a mixture that is 40% antifreeze. How much of the mixture should be drained and replaced with pure antifreeze so that the system is filled with a solution that is 50% antifreeze

Answer 1

Look at the concentrations of antifreeze

We have 40% of 15L = 0.4(15)L of antifreeze

Subtract xL from that and replace with xL of pure antifreeze

Total to 15L of 50% which is .5(15)

 

.4(15) - .4x + x = .5(15)

6 + .6x = 7.5

.6x = 1.5

x = 2.5L

 

Check:

We drain 2.5L leaving 12.5L of 40% = .4(12.5) = 5L antifreeze

We add back 2.5L of pure antifreeze giving us 7.5L of antifreeze