Respuesta :
Answer:
There would be 125 liters of 90% solution and 75 liters of 50% solution.
Step-by-step explanation:
Let x represent 90% of solution and y represent 50% of solution.
We have been given that there is 200 liters of the solution. We can represent this information in an equation as:
[tex]x+y=200...(1)[/tex]
We are also told that two hundred liters of a 75% acid solution is obtained by mixing a 90% solution with a 50% solution. We can represent this information in an equation as:
[tex]0.90x+0.50y=200(0.75)...(2)[/tex]
From equation (1), we will get:
[tex]y=200-x[/tex]
Upon substituting this value in equation (2), we will get:
[tex]0.90x+0.50(200-x)=200(0.75)[/tex]
Let us solve for x.
[tex]0.90x+100-0.50x=150[/tex]
[tex]0.40x+100=150[/tex]
[tex]0.40x+100-100=150-100[/tex]
[tex]0.40x=50[/tex]
[tex]\frac{0.40x}{0.40}=\frac{50}{0.40}[/tex]
[tex]x=125[/tex]
Therefore, there would be 125 liters of 90% solution.
Upon substituting [tex]x=125[/tex] in equation (1), we will get:
[tex]125+y=200[/tex]
[tex]125-125+y=200-125[/tex]
[tex]y=75[/tex]
Therefore, there would be 55 liters of 50% solution.
