a chemist mixed x millimeters of 25% acid solution with some 15% acid solution to produce 100 millimeters of a 19% acid solution. use this information to fill in the missing information in the table and answer the questions that follow

[tex]\left\begin{array}{c|c|c|l}&Quantity&Percent&Total\ Solution\\Solution\ 1&x&25\%=0.25&0.25x\\\underline{Solution\ 2}&\underline{\ 100-x\ }&\underline{15\%=0.15}&\underline{\qquad \quad 0.15(100-x)}\\Mixture&100&19\%=0.19&0.25x+0.15(100-x)\end{array}\right\\\\\\Mixture: 100(0.19)=0.25x+0.15(100-x)\\.\qquad \qquad \qquad 19\ \quad =0.25x+15-0.15x\\.\qquad \qquad \qquad 4\qquad =0.10x\\\\.\qquad \qquad \quad \dfrac{4}{0.10}\qquad =\dfrac{0.10}{0.10}x\\\\.\qquad \qquad \qquad 40\qquad =x[/tex]

Solution 1: x = 40

Solution 2: 100 - x --> 100 - 40 = 60

facundo3141592 facundo3141592 · Answer 2 · 2022-01-25T12:07:52+01:00

We need to find how each of each solution did the chemist mixed, and we will find that with a system of equations. We can conclude that the chemist used 40 mm^3 of the 25% solution and 60 mm^3 of the 15% solution.

Writing the system of equations.

First, we need to define the variables that we will use.

x = mm^3 of the 25% acid solution.
y = mm^3 of te 15% acid solution.

We know that at the end there are 100 mm^3 of the mixture then we must have:

x + y = 100.

We also know that the concentration of the final 100 mm^3 is 19%, then the concentration at the left must be the same than at the right, then we have:

x*0.25 + y*0.15 = 100*0.19 = 19

Where I multiplied each term by the correspondent concentration in decimal form.

Now we can see that our system of equations is:

x + y = 100

x*0.25 + y*0.15 = 19

To solve it we need to isolate one variable in one of the equations, I will isolate x on the first one:

x = 100 - y

Now we replace this on the other equation:

(100 - y)*0.25 + y*0.15 = 19

25 - y*0.10 = 19

-y*0.10 = 19 - 25 = -6

y = -6/-0.10 = 60

and:

x = 100 - y = 100 - 60 = 40

Then we can conclude that the chemist used 40 mm^3 of the 25% solution and 60 mm^3 of the 15% solution.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904