Answer:
1 : 4
Step-by-step explanation:
Let x represent the amount of 30% solution for 1 unit of 5% solution. Then the amount of acid in the mix is ...
0.30x + 0.05·1 = 0.10·(x +1)
0.30x + 0.05 = 0.10x + 0.10 . . . . eliminate parentheses
0.20x = 0.05 . . . . . . . . . . . . . . . . subtract 0.05+0.10x
x = 0.05/0.20 = 1/4
That is, the ratio x : 1 is 1 : 4.
Answer:
The ratio of the amount of the 30% solution to the amount of 5% solution will be 1 : 4.
Step-by-step explanation:
Suppose, the amount of 30% acid solution is [tex]x[/tex] and the amount of 5% acid solution is [tex]y[/tex].
So, the total amount of the mixture [tex]= x+y[/tex], which is 10% acid solution.
Amount of acid in 30% solution [tex]= 30\%\ of\ x=0.30x[/tex]
Amount of acid in 5% solution [tex]=5\%\ of\ y= 0.05y[/tex]
Amount of acid in the mixture [tex]=10\%\ of\ (x+y)=0.10(x+y)[/tex]
Now, the equation will be......
[tex]0.30x+0.05y=0.10(x+y)\\ \\ 0.30x+0.05y=0.10x+0.10y\\ \\ 0.30x-0.10x=0.10y-0.05y\\ \\ 0.20x=0.05y\\ \\ \frac{x}{y} =\frac{0.05}{0.20} =\frac{5}{20}=\frac{1}{4}\\ \\ x:y=1:4[/tex]
So, the ratio of the amount of the 30% solution to the amount of 5% solution will be 1 : 4.
