Question

A Cafeteria worker needs to make a mixture of 100 liters of 50 percent solution of apple juice. How many liters of 80 percent solution of apple juice and a 30 percent solution of apple juice are needed?

Answer 1

Answer: 40 L of 80 percent solution and 60 L of 30 percent solution

Step-by-step explanation:

The total mixture of 100 L of apple juice of $50\%$ solution must contain:

$80\%$ solution of apple juice ---> Let's call it $A$

$30\%$ solution of apple juice ---> Let's call it $B$

So, we can set these values in a table taking into account $80\%=0.8$, $30\%=0.3$ and $50\%=0.5$:

$\left[\begin{array}{ccccc}&apple-juice (L)&Percent&Total\\80\% Juice&x&0.8&0.8 x\\30\% juice&y&0.3&0.3 y\\Mixture&x+y=100&0.5&0.5(100)\end{array}\right]$

Now, with the information of the $Total$ column we can write the first equation:

$0.8 x + 0.3 y= 0.5 (100)$ (1)

And with the information of the $apple-juice$ column, the second equation:

$x + y=100$ (2)

At this point we are able to calculate how many litters have $x$ and $y$.

Isolating $y$ from (2):

$y=100-x$ (3)

Substituting (3) in (1):

$0.8 x + 0.3 (100-x)= 0.5 (100)$ (4)

$0.8 x + 30 - 0.3x= 50$

$x=40$ (5) 40 L of solution A

Substituting (5) in (2):

$40 + y=100$ (6)

$y=60$ (7) 60 L of solution B

Therefore, the cafeteria worker needs to mix 40 L of solution A with 60 L of solution B.