Respuesta :
Answer:
Concentration of solutions A and B are 33% and 7% respectively.
Step-by-step explanation:
Suppose, the concentration of solutions A and B are [tex]x[/tex] and [tex]y[/tex] respectively.
First mixture
Ratio of solutions A and B is 1 : 1
Lets assume the amount of solution A is [tex]1v[/tex] and amount of solution B is [tex]1v[/tex]
Total amount of first mixture [tex]=1v+1v=2v[/tex] and concentration of first mixture is 20%
So, the first equation will be.......
[tex]2v\times 0.20= (1v \times x)+(1v\times y)\\ \\ 0.40v=vx+vy\\ \\ x+y=0.40 .......................(1)[/tex]
Second mixture
Ratio of solutions A and B is 3 : 7
Lets assume the amount of solution A is [tex]3v[/tex] and amount of solution B is [tex]7v[/tex]
Total amount of first mixture [tex]=3v+7v=10v[/tex] and concentration of first mixture is 14.8%
So, the second equation will be.......
[tex]10v\times 0.148= (3v \times x)+(7v\times y)\\ \\ 1.48v=3vx+7vy\\ \\ 3x+7y=1.48 .......................(2)[/tex]
From equation (1), we will get : [tex]y=0.40-x[/tex]
Now substituting this [tex]y=0.40-x[/tex] into equation (2)......
[tex]3x+7(0.40-x)=1.48\\ \\ 3x+2.80-7x=1.48\\ \\ -4x=1.48-2.80\\ \\ -4x=-1.32\\ \\ x=\frac{-1.32}{-4}=0.33[/tex]
Plugging this [tex]x=0.33[/tex] into equation (1), we will get......
[tex]0.33+y= 0.40\\ \\ y=0.40-0.33=0.07[/tex]
So, the concentration of solution A is 0.33 or 33% and the concentration of solution B is 0.07 or 7%
