Lisa will make punch that is 25% fruit juice by adding pure fruit juice to a 2-liter mixture that is 10% pure fruit juice. How many liters of pure fruit juice does she need to add?
1 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%)CfinalVfinal=CpureVpure+C25%V25%
where
-
C_"final"Cfinal andV_"final"Vfinal are the concentration and volume of the final solution. We're given that the final concentration must be25%25% . -
C_"pure"Cpure andV_"pure"Vpure are the concentration and volume of the pure solution. We'll say that a pure solution has a concentration of11 . -
C_(25%)C25% andV_(25%)V25% are the concentration and volume of the25%25% solution. We're given both of these quantities as0.100.10 and22 "L"L respectively.
Plugging in all known values, we have
0.25(V_"final") = 1(V_"pure") + 0.10(2color(white)(l)"L")0.25(Vfinal)=1(Vpure)+0.10(2lL)
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"Vfinal=Vpure+2lL
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")0.25(Vpure+2lL)=Vpure+0.10(2lL)
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(Vpure)+0.5lL=Vpure+0.2lL
0.25(V_"pure") + 0.3color(white)(l)"L" = V_"pure"0.25(Vpure)+0.3lL=Vpure
Divide all terms by
0.25 + (0.3color(white)(l)"L")/(V_"pure") = 10.25+0.3lLVpure=1
(0.3color(white)(l)"L")/(V_"pure") = 0.750.3lLVpure=0.75
color(red)(ulbar(|stackrel(" ")(" "V_"pure" = 0.4color(white)(l)"L"" ")|)