How many liters of 70% solution must be mixed with 100 liters of 40% solution to get to a mixture of 50% solution?

Question

How many liters of 70% solution must be mixed with 100 liters of 40% solution to get to a mixture of 50% solution?

Answer 1

Lets call this unknown x, so if we take x liters of 70% and add 100 liters of 40%, we have .7x+40 liters of concentrate and we want that to be 50% of the volume of solution we mixed, which is 100+x, so we need:

 

.7x+40 = (1/2)(100+x)=50+.5x

Rearranging we get .2x=10 or x=50.