# One canned juice drink is 20% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 15L that is 17% orange juice?

May 29, 2017

12 litres of the 20% drink, and 3 litres of the 5% drink

#### Explanation:

Let's say that $x$ is how many litres of the 20% drink.
And that $y$ is the number of litres of the 5% drink.

From this we can write the first equation:
$x + y = 15$, as we know that total there should be 15 litres.

Next we can write an equation for the concentration:
$\frac{20}{100} x + \frac{5}{100} y = \frac{17}{100} \cdot 15$, this times the concentration, and finds the actual amount of orange juice in each equation.

Next we need to rearrange one to substitute in, and the first equation is probably easier to rearrange.

$x + y = 15$
Take away y from both sides:
$x + y - y = 15 - y$
$x = 15 - y$

Then substitute in to the second equation for the x value:
$\frac{20}{100} \left(15 - y\right) + \frac{5}{100} y = \frac{17}{100} \cdot 15$

Expand and simplify:
$3 - 0.15 y = 2.55$

Then solve for $y$:
$- 0.15 y = - 0.45$
$y = 3$

Then solve for $x$:
$x + y = 15$
$x + 3 = 15$
$x = 12$

So 12 litres of the 20% drink, and 3 litres of the 5% drink.