A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar and the second brand contains 15% vinegar. The chef wants to make 280 milliliters of a dressing that is 14% vinegar. How much of each brand should she use?

Question

Mathematics

Janiya Oliver

28 February, 19:23

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar and the second brand contains 15% vinegar. The chef wants to make 280 milliliters of a dressing that is 14% vinegar. How much of each brand should she use?

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Answers (1)

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Kaeden Cooke · Answer 1

35ml of the first brand

245ml of the second brand

Step-by-step explanation:

The chef wishes to use two brands of an Italian dressing

The first brand constitutes of 7% vinegar

Let A represent the first brand

The second brand contains 15% vinegar

Let B represent the second brand

280 militers of dressing will be used to preoare both the first and second brands

A+B=280

The total mixture contains 14% vinegar, therefore it will be represented as

0.07A+0.15B = 0.14*280

0.07+0.15B = 39.2

We have to find the value of A and B inorder to get the amount of both brands.

0.07A+0.15B=39.2

0.07A + 0.15 (280-A) = 39.2

0.07A+42-0.15A=39.2

Collect the co-efficient for both sides

0.07A-0.15B=39.2-42

-0.08A = - 2.8

Divide both sides by - 0.08

-0.08A/-0.08 = - 2.8/-0.08

A=35

To find B, substitute 35 for A in the equation below

A+B=280

35+B=280

B = 280-35

B = 245

Thus, the chef will be needing 35ml of the first brand and 245ml of the second brand.