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?

Question

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

Impact of this question

2810 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-02T14:20:54

$0.4$ $0.4$ $L$ $"L"$ must be added.

Explanation:

We're asked to find the volume (in liters) of $100 %$ $100%$ fruit juice that must be added to $1$ $1$ $L$ $"L"$ of a $10 %$ $10%$ fruit juice mixture so that the final concentration is $25 %$ $25%$ .

To do this, we can use the following relationship:

$C_{final} V_{final} = C_{pure} V_{pure} + C_{25 %} V_{25 %}$ $C_"final"V_"final" = C_"pure"V_"pure" + C_(25%)V_(25%)$

where

$C_{final}$ $C_"final"$ and $V_{final}$ $V_"final"$ are the concentration and volume of the final solution. We're given that the final concentration must be $25 %$ $25%$ .
$C_{pure}$ $C_"pure"$ and $V_{pure}$ $V_"pure"$ are the concentration and volume of the pure solution. We'll say that a pure solution has a concentration of $1$ $1$ .
$C_{25 %}$ $C_(25%)$ and $V_{25 %}$ $V_(25%)$ are the concentration and volume of the $25 %$ $25%$ solution. We're given both of these quantities as $0.10$ $0.10$ and $2$ $2$ $L$ $"L"$ respectively.

Plugging in all known values, we have

$0.25 (V_{final}) = 1 (V_{pure}) + 0.10 (2 l L)$ $0.25(V_"final") = 1(V_"pure") + 0.10(2color(white)(l)"L")$

Volumes here are going to be additive; that is, the final volume will be the sum of the volumes of the two components:

$V_{final} = V_{pure} + 2 l L$ $V_"final" = V_"pure" + 2color(white)(l)"L"$

We'll now plug this into the equation for $V_{final}$ $V_"final"$ :

$0.25 (V_{pure} + 2 l L) = V_{pure} + 0.10 (2 l L)$ $0.25(V_"pure" + 2color(white)(l)"L") = V_"pure" + 0.10(2color(white)(l)"L")$

Now, we just solve for the necessary volume, $V_{pure}$ $V_"pure"$ :

$0.25 (V_{pure}) + 0.5 l L = V_{pure} + 0.2 l L$ $0.25(V_"pure") + 0.5color(white)(l)"L" = V_"pure" + 0.2color(white)(l)"L"$

$0.25 (V_{pure}) + 0.3 l L = V_{pure}$ $0.25(V_"pure") + 0.3color(white)(l)"L" = V_"pure"$

Divide all terms by $V_{pure}$ $V_"pure"$ :

$0.25 + \frac{0.3 l L}{V_{pure}} = 1$ $0.25 + (0.3color(white)(l)"L")/(V_"pure") = 1$

$\frac{0.3 l L}{V_{pure}} = 0.75$ $(0.3color(white)(l)"L")/(V_"pure") = 0.75$

$color(red)(ulbar(|stackrel(" ")(" "V_"pure" = 0.4color(white)(l)"L"" ")|)$

Science

Math

Humanities

... and beyond

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:

Related questions

Impact of this question