I recently took my math midterms, when I came across this problem that I always forget to do.. Just to ease my mind, I'd like someone to answer this question with work shown step by step.

How many liters of 20% alcohol solution would you require to make a 70% alcohol solution into 60% alchohol?

Question

I recently took my math midterms, when I came across this problem that I always forget to do.. Just to ease my mind, I'd like someone to answer this question with work shown step by step.

How many liters of 20% alcohol solution would you require to make a 70% alcohol solution into 60% alchohol?

phi · Answer

You do not get a definite answer unless you know how much of the 70% solution you start with.  It takes much less of the 20% solution to dilute 1 liter than 100 liters.

But if you say we will end up with 1 liter of the 60% alcohol solution we can do this:
let x be the liters of 20% solution
     y                         70% solution
and x+y= 1  (we want to get a total of 1 liter when added together)
the amount of alcohol in each solution is
0.2x + 0.7y = 0.6*1  or simplifying 2x+7y= 6
you now have two equations and two unknowns:

2x + 7y = 6
  x  +  y  =1

solve for x and y