Answer:
I think that the answer is
b = 7
Here is the step-by-step solution.....
See the attached files for the step-by-step solution...><><
23
Those are not the answer:
1) 20 - can be divided by 2
2) 21 - can be divided by 3
3) 22 - can be divided by 2
4) 24 - can be divided by 2 and 4.
5) 25 - can be divided by 5
6) 26 - can be divided by 2
7) 27 - can be divided by 3
8) 28 - can be divided by 2 and 4
Let x represent the number of liters of 50% acid Theresa puts into the mix. The the number of liters of 30% acid will be (420-x). The total amount of acid in the final solution will be ...
0.50x + 0.30(420-x) = 0.45(420)
0.20x + 126 = 189 . . . . . . . . . . . . . . . simplify
0.20x = 63 . . . . . . . . . . . . . . . . . . . . . subtract 126
x = 63/0.20 = 315 . . . . . . . . . . . . . . . liters of 50% solution
(420-x) = 420-315 = 105 . . . . . . . . . liters of 30% solution
Theresa should mix ...
105 liters of 30% solution
315 liters of 50% solution
By definition, we have

So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:
Suppose that 
In this case, the absolute value doesn't do anything: the equation is

We are supposing
, so we can accept this solution.
Now, suppose that
. Now the sign of the expression is flipped by the absolute value, and the equation becomes

Again, the solution is coherent with the assumption, so we can accept this value as well.