Question 1035164
.
A chef is using a mixture of two brands of Italian dressing. The first brand contains 6% vinegar, and the second brand 
contains 11% vinegar. The chef wants to make 210 milliliters of a dressing that is 8% vinegar. How much of each brand should she use? 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
     x +      y = 210,         (1)
0.06*x + 0.11*y = 0.08*210,    (2)

Multiply (1) by 100 and simplify. You will get the modified system

  x +    y =  210,            (1')
6*x + 11*y = 1680.            (2')

Solve it by using the Substitution method.
From (1') express x = 210 - y and substitute into (2'). You will get a single equation

6*(210-y) + 11y = 1680,

1260 - 6y + 11y = 1680,

5y = 1680-1260,

5y = 420,

y = {{{420/5}}} = 84.

<U>Answer</U>. 84 milliliters of the 11% vinegar and 210-84 = 126 milliliters of the 6% vinegar.

<U>Check</U>. 0.06*126 + 0.11*84 = 16.80.   Correct!
</pre>