Question

how many liters of each of a 15% acid solution and a 25% acid solution must be used to produce 80 liters of a 20% acid solution?

Answer 1

Given:

Total produce = 80 liters

15% Acid solution and 25% acid solution

Find-:

How many litres of each

Explanation-:

Let

`\begin{gathered} x=\text{ Liters of }15\% \\ \\ y=\text{ Liters of }25\% \end{gathered}`

Total 80 litres

`x+y=80............(1)`
`\begin{gathered} 15x+25y=80*20 \\ \\ 3x+5y=320..............(2) \end{gathered}`

eq(2) - 3eq(1) is:

`\begin{gathered} x+y=80 \\ \\ 3x+3y=240..........(1^(\prime)) \end{gathered}`

So, the value of "y" is:

`\begin{gathered} 3x+5y-3x-3y=320-240 \\ \\ 2y=80 \\ \\ y=(80)/(2) \\ \\ y=40 \end{gathered}`

So x is 40

Then,

`\begin{gathered} 40\text{ liters of }15\%\text{ acid solution } \\ \\ 40\text{ liters of }25\%\text{ acid soluion} \end{gathered}`