Question 242296
I am a visual learner, so I try to draw a picture to help me understand a word problem.  In a mixture problem, you are working with an amount(ml) and a concentration(%).

I draw 3 lines ___+___=___ (I usually use boxes instead of lines to combine the #'s and variables) 
Let your first brand = x
Let your second brand = y
You do not need a variable for the product because you have an amount and a concentration already.  Use the variables (x and y) to replace your unknowns.  The unknowns are the amounts of the first and second brands.

x+y=320 (this is your equation for the amounts)
0.08x +0.13y=.11(320) (this is your equation for the concentrations)

We can use the substitution or elimination method to solve this.  I will use the substitution method.  I don't like using decimals, so I am going to move the decimal place two units to the right to make them whole numbers.  This gives me: 8x+13y=11(320)

Using substitution on the first equation, I put X on one side of the equation.  This gives me x=(-y+320).  I can now substitute (-y+320) for x in the second equation.

8(-y+320)+13y=3520
-8y+2560+13y=3520
Subtract 2560 from both sides and combine 13y and -8y.  This gives you 5y=960.  Divide both sides of the equation by 5.  This gives you y=192.

y=192
x=128

I got x by plugging y into equation #1.
x+(192)=320. After subtracting 192 from 320, I get x= 128.
To check your answer, always substitute x and y in for both equations.
ANSWER: The chef should use 128 milliliters of the 8% vinegar brand and 192 milliliters of the 13% vinegar brand.