Setting up Equations for Mixture Problem

Question

An automobile radiator contains 16 liters of antifreeze and water. This mixture is 30% antifreeze. How much of this mixture should be drained and replaced with pure antifreeze so that there will be 50% antifreeze?

I can obtain the answer using my own method of solving this problem, but the problem is that I need to set up equations for this, looking for help, thanks

Answer 1

Hint:

You can have a solution whatever the volume $V$ of mixture: suppose you replace a fraction $xV$ of mixture with the same volume of pure antifreeze. The total volume of pure antifreeze in the new mixture is $\;0.3(1-x)V+xV=(0.3+0.7x)V$, hence the equation will be $$0.3+0.7x=0.5$$