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

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.