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
[tex]y = \frac{440}{5} = 88[/tex]
Substituting y = 88 in eqn (2),
7x + 7( 88 ) = 1540
7x + 616 = 1540
7 x = 1540 - 616 = 924
[tex]x = \frac{924}{7} = 132[/tex]
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.
