a chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar and the second Brian con

Question

3 years ago

7

a chef is going to use a mixture of two brands of Italian dressing. The first brand contains 5% vinegar and the second Brian con

tains 15% vinegar. The chef wants to make 390 mL of a dressing that is 8% vinegar. How much of each brand should she use?

Mathematics

1 answer:

tankabanditka [31] · Answer 1 · 2022-06-08T03:54:16+03:00

Answer:

273 mL of 5%
117 mL of 15%

Step-by-step explanation:

Let q represent the quantity of 15% dressing used. Then the amount of 5% dressing is (390 -q). The amount of vinegar in the mix is ...

0.15q + 0.05(390 -q) = 0.08(390)

0.10q = 31.2 -19.5 = 11.7 . . . . . . subtract 0.05(390) and simplify

q = 117 . . . . . . . . . . . . . . . . . . multiply by 10

390-q = 273

The chef should use 273 mL of the first brand (5% vinegar) and 117 mL of the second brand (15% vinegar).

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<em>Additional comment</em>

You may have noticed that the value of q is (0.08 -0.05)/(0.10 -0.05)×390. The fraction of the mix that is the highest contributor is the ratio of the difference between the mix value and least contributor, divided by the difference between the contributors: (8-5)/(15-5) = 3/10, the fraction that is 15% vinegar. This is the generic solution to mixture problems.