A chemist needs to create a 25% citrus mixture by adding 20 mL of a 80% citrus solution to a 5% citrus solution. How much of each is needed?

1 Answer
Aug 25, 2015

Answer:

You would have to use 55 mL of 5 % citrus solution, and we would get 75 mL of 25 % citrus solution.

Explanation:

80 % citrus means #"80 mL citrus"/"100 mL solution"#

So in 20 mL of 80 % citrus:

#"Volume of citrus" = 20 color(red)(cancel(color(black)("mL soln"))) × "80 mL citrus"/(100 color(red)(cancel(color(black)("mL soln")))) = "16 mL citrus"#

In #x " mL"# of 5 % citrus,

#"Volume of citrus" = x color(red)(cancel(color(black)("mL soln"))) × "5 mL citrus"/(100 color(red)(cancel(color(black)("mL soln")))) = x/20 " mL citrus"#

We add #x " mL"# of 5 % citrus to #"20 mL"# of 80 % citrus to get #20+x " mL"# of 25 % citrus.

#"Total volume of citrus" = (16 + x/20) " mL"#

#"Total volume of solution" = (20+x) " mL"#.

#(16+x/20)/(20+x) = 25/100#

#100(16+x/20)= 25(20+x)#

#1600+5x=500+25x#

#20x = 1600-500 =1100#

#x = 1100/20#

#x = 55#

We have to add 55 mL of 5 % citrus to 20 mL of 80 % citrus and get 75 mL of 25 % citrus.

Check:

#(16+55/20)/(20+55) = 25/100#

#((320 +55)/20)/75 = 25/100#

#375/1500 = 25/100#

#1/4=1/4#

It checks!