Question

A scientist needs 120 ML of a 20% acid solution for an experiment. The lab has available at 10% solution and a 25% solution. How many milliliters of the 10% solution and how many milliliters of a 25% solution should the scientist mix to make the 20% solution?

Answer 1

40 milliliters of the 10% solution and 80 milliliters of the 25% solution the scientist should mix to make the 20% solution.

Explanation:

Given:

A scientist needs 120 ML of a 20% acid solution for an experiment. The lab has available at 10% solution and a 25% solution.

Now, to find the milliliters of 10% solution and 25% solution to make 20% solution:

Let the 10% solution be
`x.`

And let the 25% solution be
`y.`

So, total milliliters of solution are:

`x+y=120\\\\x=120-y\ \ \ \ .....(1)`

Now, to get the milliliters of 10% solution and 25% solution to make 20% solution we solve the equation:

`10\%\ of\ x+25\%\ of\ y=20\%\ of\ 120\\\\(10)/(100) * x+(25)/(100) * y=(20)/(100) * 120\\\\0.10x+0.25y=24`

Substituting the value of
`x` from equation (1) we get:

`0.10(120-y)+0.25y=24\\\\12-0.10y+0.25y=24\\\\12+0.15y=24`

Subtracting both sides by 12 we get:

`0.15y=12`

Dividing both sides by 0.15 we get:

`y=80.`

Thus, the 25% solution is 80 ml.

Now, substituting the value of
`y` in equation (1) we get:

`x=120-y\\\\x=120-80\\\\x=40\ ml.`

Hence, the 10% solution is 40 ml.

Therefore, 40 milliliters of the 10% solution and 80 milliliters of the 25% solution the scientist should mix to make the 20% solution.