Respuesta :
Answer:
40 milliliters of the 10% solution and 80 milliliters of the 25% solution the scientist should mix to make the 20% solution.
Step-by-step 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 [tex]x.[/tex]
And let the 25% solution be [tex]y.[/tex]
So, total milliliters of solution are:
[tex]x+y=120\\\\x=120-y\ \ \ \ .....(1)[/tex]
Now, to get the milliliters of 10% solution and 25% solution to make 20% solution we solve the equation:
[tex]10\%\ of\ x+25\%\ of\ y=20\%\ of\ 120\\\\\frac{10}{100} \times x+\frac{25}{100} \times y=\frac{20}{100} \times 120\\\\0.10x+0.25y=24[/tex]
Substituting the value of [tex]x[/tex] from equation (1) we get:
[tex]0.10(120-y)+0.25y=24\\\\12-0.10y+0.25y=24\\\\12+0.15y=24[/tex]
Subtracting both sides by 12 we get:
[tex]0.15y=12[/tex]
Dividing both sides by 0.15 we get:
[tex]y=80.[/tex]
Thus, the 25% solution is 80 ml.
Now, substituting the value of [tex]y[/tex] in equation (1) we get:
[tex]x=120-y\\\\x=120-80\\\\x=40\ ml.[/tex]
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.
