Given the word problem, we can deduce the following information:
1. A chemist has 20% and 50% solutions of acid.
2. The solution should be mixed to obtain 93.75 liters of 28% acid solution.
To determine the amount of liters of each solution, the equation we should use is:
[tex]\begin{gathered} 0.2x+0.5(93.75-x)=0.28(93.75) \\ \end{gathered}[/tex]
where:
x= amount of liters
We simplify the equation and rearrange to get the value of x:
[tex]\begin{gathered} 0.2x+0.5(93.75-x)=0.28(93.75) \\ 0.2x+46.875-0.5x=26.25 \\ -0.3x+46.875=26.25 \\ -0.3x=26.25-46.875 \\ -0.3x=-20.625 \\ x=-\frac{20.625}{-0.3} \\ x=68.75\text{ Liters} \end{gathered}[/tex]
For 20% acid, the amount in liters is 68.75. While to get for 50% acid is by:
93.75-68.75 = 25 Liters
Therefore, the answer is:
68.75 liters for 20% acid
25 liters for 50% acid.
