Lisa will make punch that is 25% fruit juice by adding pure fruit juice to a 2liter mixture that is 10% pure fruit juice. How many liters of pure fruit juice does she need to add?
1 Answer
Answer:
Explanation:
We're asked to find the volume (in liters) of
To do this, we can use the following relationship:
#C_"final"V_"final" = C_"pure"V_"pure" + C_(25%)V_(25%)#
where

#C_"final"# and#V_"final"# are the concentration and volume of the final solution. We're given that the final concentration must be#25%# . 
#C_"pure"# and#V_"pure"# are the concentration and volume of the pure solution. We'll say that a pure solution has a concentration of#1# . 
#C_(25%)# and#V_(25%)# are the concentration and volume of the#25%# solution. We're given both of these quantities as#0.10# and#2# #"L"# respectively.
Plugging in all known values, we have
#0.25(V_"final") = 1(V_"pure") + 0.10(2color(white)(l)"L")#
Volumes here are going to be additive; that is, the final volume will be the sum of the volumes of the two components:
#V_"final" = V_"pure" + 2color(white)(l)"L"#
We'll now plug this into the equation for
#0.25(V_"pure" + 2color(white)(l)"L") = V_"pure" + 0.10(2color(white)(l)"L")#
Now, we just solve for the necessary volume,
#0.25(V_"pure") + 0.5color(white)(l)"L" = V_"pure" + 0.2color(white)(l)"L"#
#0.25(V_"pure") + 0.3color(white)(l)"L" = V_"pure"#
Divide all terms by
#0.25 + (0.3color(white)(l)"L")/(V_"pure") = 1#
#(0.3color(white)(l)"L")/(V_"pure") = 0.75#
#color(red)(ulbar(stackrel(" ")(" "V_"pure" = 0.4color(white)(l)"L"" "))#