Question

Jotham needs 70 liters of a 50% alcohol solution. He has a 30% solution and an 80% solution available. How many liters of

the 30% solution and how many liters of the 80% solution should he mix to make the 50% solution?

Answer 1

x+y=70. (30x+80y)/(100x+100y)=50/100

Answer 2

42 liters of 30% alcohol solution will be needed.

28 liters of 80% solution will be needed.

Explanation:

Jotham needs 70 liters of a 50% alcohol solution.

Let the 30% solution needed be x.

We get the following equation:

`70*0.5=0.30x+0.80(70-x)`

Solving this we get;

`35=0.30x+56-0.80x`

=>
`35=56-0.50x`

=>
`0.50x=56-35`

=>
`0.50x=21`

x = 42

Hence, 42 liters of 30% alcohol solution will be needed.

And
`70-42=28` liters of 80% solution will be needed.