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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?

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 class=

Sagot :

Given:

Total produce = 80 liters

15% Acid solution and 25% acid solution

Find-:

How many litres of each

Explanation-:

Let

[tex]\begin{gathered} x=\text{ Liters of }15\% \\ \\ y=\text{ Liters of }25\% \end{gathered}[/tex]

Total 80 litres

[tex]x+y=80............(1)[/tex][tex]\begin{gathered} 15x+25y=80\times20 \\ \\ 3x+5y=320..............(2) \end{gathered}[/tex]

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

[tex]\begin{gathered} x+y=80 \\ \\ 3x+3y=240..........(1^{\prime}) \end{gathered}[/tex]

So, the value of "y" is:

[tex]\begin{gathered} 3x+5y-3x-3y=320-240 \\ \\ 2y=80 \\ \\ y=\frac{80}{2} \\ \\ y=40 \end{gathered}[/tex]

So x is 40

Then,

[tex]\begin{gathered} 40\text{ liters of }15\%\text{ acid solution } \\ \\ 40\text{ liters of }25\%\text{ acid soluion} \end{gathered}[/tex]

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