one canned juice drink is 25% orange juice; another is 5% orange juice. how many liters of each should be mixed together in order to get 20L that is 10% orange juice?

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pphalke · Answer

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pphalke · Answer

@jim_thompson5910

pphalke · Answer

@mathstudent55 @HyperPiper @ganeshie8

mathstudent55 · Answer

Let's choose two variables to represent the amounts of the two juices.
Let x be the amount of 25% juice needed, and let y be the amount of 5% juice needed.

We want to make 20 L of juice mixture, so that gives us our first equation:

$x + y = 20$

mathstudent55 · Answer

Now let's look at the actual amount of juice in each drink using the amounts we will use and their concentrations.

We will use x liters of 25% drink; that has 0.25x liters of actual juice.
We will use y liters of 5% drink; that has 0.05y liters of actual juice.
We will end up with 10 L of 20% drink. That has 0.10 * 20 = 2 L of actual juice.

This gives us the second equation:

0.25x + 0.05y = 2

mathstudent55 · Answer

Now we have a system of equations:

$x + y = 20$

$0.25x + 0.05y = 2$

Solve the first equation for y: $y = 20 - x$
Substitute 20 - x for  y in the second equation:

$0.25x + 0.05(20 - x) = 2$

$0.25x + 1 - 0.05x = 2$

$0.2x + 1 = 2$

$0.2x = 1$

$\dfrac{0.2x}{0.2} = \dfrac{1}{0.2} $

$x = 5$

Now we solve for y:

$x + y = 20$

$5 + y = 20$

$y = 15$

Answer: 5 liters of 25% drink and 15 liters of 5% drink.