A chef is going to use a mixture of two brands of italian dressing. the first brand contains 9% vinegar, and the second brand contains 15% vinegar. the chef wants to make 330 milliliters of a dressing that is 11% vinegar. how much of each brand should she use?

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08-08-2017
Chemistry

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A chef is going to use a mixture of two brands of italian dressing. the first brand contains 9% vinegar, and the second brand contains 15% vinegar. the chef wants to make 330 milliliters of a dressing that is 11% vinegar. how much of each brand should she use?

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Edufirst Edufirst · Answer 1 · 2017-08-16T04:33:57+02:00

Call x the volume of first brand (9% vinegar) and y the volume of the second brand (15% vinegar).

1) Balance on vinegar content:

x*9% + y*15% = 330 * 11%

=> 9x + 15y = 3630 ---- Equation (1)

2) Balance on volume of dressing:

x + y = 330 ---- Equation (2)

3) Mulitply equation (2)

9x + 9y = 2970

4) subtract from equation (1)

=> 15y - 9y = 3630 - 2970

=> 6y = 660

=> y = 660 / 6

=> y = 110 ml

5) replace y value in the equation (2)

x + 110 = 330

=> x = 330 - 110

=> x = 220 ml.

Answer: he should use 220 ml of the first brand (9% vinegar) and 110ml of the second brand (15% vinegar).