Lets call x the amount of 18% solution and y the amount of 40% solution, and write as equations the info of the problem:
18x + 40y = 10(20)
x + y = 10
lets multiply the second equation by -18 and add to the first:
18x + 40y = 200
-18x -<span> 18y = -180
</span>----------------------
0 + 22y = 20
y = 20/22 = 10/11
and substitute in the original equation:
x <span>+ y = 10
</span>x = 10 - y
x = 10 - 10/11
x = 110/11 - 10/11
x = 100/11
so they have to use 100/11 liters of 18% solution and 10/11 liters of 40% solution
You haven't provided the expression or the choices, therefore, I cannot provide an exact answer.
However, I'll try to help you understand the concept so that you can solve the question you have
Like radicals are characterized by the following:1- They both have the same root number (square root, cubic root , ...etc)
2- They both have the same radicand (meaning that the expression under the root is the same in both radicals)
Examples of like radicals:3

and 7

![\sqrt[5]{x^2y}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7Bx%5E2y%7D%20)
and 3
![\sqrt[5]{x^2y}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7Bx%5E2y%7D%20)
Check the choices you have. The one that satisfies the above two conditions would be your correct choice
Hope this helps :)
She forgot about the final x at the end, because the first expression is 3x+6+x, and the second one is 3(x+2). The second one expands to 3x+6, but it doesn't have the final term at the end.
Also, 3 is not really a factor of x (technically it could be because x in unknown, but in terms of like terms and stuff it isn't) so you can't take a 3 out of x (unless you leave it as 1/3x I guess).
Anyway, yeah she forgot about the final x and therefore the factor she took out is incorrect anyway. She also could've simplified the first expression so that it became 4x + 6