Question

In a lab, a 30% acid solution is being mixed with a 5% acid solution to create a 10% acid solution. What is the ratio of the amount of the 30% solution to the amount of 5% solution used to create the 10% solution? 1:3 1:4 1:5 1:6

Answer 1

The ratio of the amount of the 30% solution to the amount of 5% solution will be 1 : 4.

Explanation:

Suppose, the amount of 30% acid solution is
`x` and the amount of 5% acid solution is
`y`.

So, the total amount of the mixture
`= x+y`, which is 10% acid solution.

Amount of acid in 30% solution
`= 30\%\ of\ x=0.30x`

Amount of acid in 5% solution
`=5\%\ of\ y= 0.05y`

Amount of acid in the mixture
`=10\%\ of\ (x+y)=0.10(x+y)`

Now, the equation will be......

`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\\ \\ (x)/(y) =(0.05)/(0.20) =(5)/(20)=(1)/(4)\\ \\ x:y=1:4`

So, the ratio of the amount of the 30% solution to the amount of 5% solution will be 1 : 4.

Answer 2

1 : 4

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.