We want to create 50 liters of 45% concentrated acid. We have two solutions - one is 30% acid and the other is 60% acid. How much of each is needed to create our desired solution?

1 Answer

Answer:

25 litres of each of the 30% and 60% solutions will produce the required 50 litres of 45% acid

Explanation:

We have the following situation:

#((color(white)(000),litres, acid %),("want",50,45%),("have",x,30%),("have",y,60%))#

where #x="amount of 30% acid", y="amount of 60% acid"#

From this chart, we can see two things:

  • #x+y=50#
  • #.3x+.6y=.45(50)#

To solve, I'm going to take the first equation and solve for #x# in terms of #y#:

#x=50-y#

and now substitute it into the second equation:

#.3(50-y)+.6y=.45(50)#

#15-.3y+.6y=22.5#

#.3y=7.5#

#y=7.5/.3#

#color(blue)ul( bar( abs( color(black)("y=25"))))#

which means that:

#x=50-25#

#color(blue)ul( bar( abs( color(black)("x=25"))))#