Question 710493
This and so many like it can all be done through assigning variables, solving for the unknown variable or variables, and then substitute the known values to finish the answer.  


I'll do this one mostly through the use of the known values with the unknowns directly, and then solve the system.


x and y, for pounds of Brand B and Brand A, in that order (remember, brand B has less percent peanuts than brand A).


Account for the peanuts.
x*30+y*25


Account for the total 20 pounds of mixture.
x+y=20


Wanted, 27% peanuts:
{{{(x*30+y*25)/20=27}}}
AND
{{{x+y=20}}}
Solve the system.


30x+25y=20*27
30x+25(20-x)=20*27, did a substitution for y from the 20pounds equation.
.
skipping steps for brevity,
{{{highlight(x=8)}}}, for Brand B
therefore {{{highlight(y=12)}}} for Brand A.