Achef is going to use a mixture of two brands of italian dressing. the first brand contains  7% vinegar, and the second brand contains  12%  vinegar. the chef wants to make  220 milliliters of a dressing that is  9%  vinegar. how much of each brand should she use?

ANSWER:  

132 ml of 7% vinegar of first brand must be mixed with 88 ml of 12% vinegar of second brand to obtain 220 ml of 9% vinegar.

SOLUTION:  

First, set up table. Fill in the unknowns with variables x and y. The table is attached below.

From the table, we can easily set up the two equations.  

Sum of values of two brands vinegar = Value of mixture  

0.07x+0.12y=19.8

For convenience, we'll multiply the entire equation by 100,

7 x + 12 y = 1980 ------ eqn (1)  

Now, Sum of amounts of each vinegar brand = Amount of mixture  

x + y = 220 --------- eqn (2)

multiply  eqn (2) with 7 for easy calculation and derive the equation into one variable.

7x + 7y = 1540  ---- eqn 3

Subtracting equation (3) from (1),  

0 + 5y = 440  

Thus,  

5y = 440  

Substituting y = 88 in eqn (2),

7x + 7( 88 ) = 1540  

7x + 616 = 1540

7 x = 1540 - 616 = 924

So, we have x = 132 and y = 88

We can conclude that 132 ml of 7% vinegar of first brand must be mixed with 88 ml of 12% vinegar of second brand to obtain 220 ml of 9% vinegar.