Answer:
- 150 mL of the second brand (13%)
- 50 mL of the first brand (9%)
Step-by-step explanation:
Let x represent the number of mL of the second brand the chef should use. The amount of vinegar in the mix is ...
9%(200 -x) +13%(x) = 12%(200)
Subtracting 9%×200 and simplifying, we get ...
(13% -9%)x = 200(12% -9%)
Dividing by the coefficient of x gives ...
x = 200(12% -9%)/(13% -9%) . . . see note below
x = 200(3/4) = 150 . . . . mL of brand 2.
The chef should use 50 mL of brand 1 and 150 mL of brand 2.
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Note on the solution
The generic solution for such a mixture problem is that the fraction of the mix that is the highest contributor (brand 2, in this case) is the ratio of two differences. The numerator is the difference between the mix percentage and that of the smallest percentage being contributed. The denominator is the difference between the percentages being contributed.
Knowing this, you can write down the answer that the 13% brand makes up (12-9)/(13-9) = 3/4 of the mix. 3/4 of 200 mL is 150 mL of brand 2, leaving 50 mL of brand 1.
