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Sagot :
Given:
There are given that the Jotham needs 12 litters of 20% alcohol solution.
Explanation:
Let x be the volume of the 50% solution needed
Then,
The volume of the 10% solution to mix is:
[tex](12-x)[/tex]Then,
The equation to find x is:
[tex]0.50x+0.10\times(12-x)=0.20\times12[/tex]That means,
It say that the volume of the pure alcohol in ingredients is equal to the volume of pure alcohol.
Then,
From the above equation, calculate the value of x
So,
[tex]\begin{gathered} 0.50x+0.10\times(12-x)=0.20\times12 \\ 0.50x+0.10\cdot12-0.10x=0.20\cdot12 \\ 0.40x+0.10\cdot12=0.20\cdot12 \\ 0.40x=0.20\cdot12-0.10\cdot12 \\ x=\frac{12(0.1)}{0.40} \\ x=3 \end{gathered}[/tex]Final answer:
For the 50%, there are 3 litters solution and for the 10%,
[tex]\begin{gathered} 12-x=12-3 \\ =9 \end{gathered}[/tex]Hence, 3 liters of the 50% solution and 9 liters of the 10% solution.
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