20 pts and a mark for ! 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 13 % vinegar. the chef wants to make 200 milliliters of a dressing that is 12 % vinegar. how much of each brand should she use?

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.

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.

7. 153.86 ft

8. 12.56 ft

9. 78.5 m

10. 379.94 in

11. 132.665 m

12. 12.56 yd

13. 226.865 ft

14. 113.04 ft

15. 63.585 ft

16. 254.34 m

17. 50.24 cm

step-by-step explanation:

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1. 22

2. 1

3. 7

4. 18

step-by-step explanation

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