Question

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 12% vinegar. The chef wants to make 270 milliliters of a dressing that is 11% vinegar. How much of each brand should she use?

Answer 1

54 and 216

Explanation:

If x is the amount of 7% vinegar, and y is the amount of 12% vinegar, then the total volume is:

x + y = 270

And the total amount of vinegar is:

0.07x + 0.12y = 0.11 (270)

0.07x + 0.12y = 29.7

Solve the system of equations. Using substitution:

0.07x + 0.12 (270 − x) = 29.7

0.07x + 32.4 − 0.12x = 29.7

0.05x = 2.7

x = 54

y = 216

The chef needs 54 mL of the 7% vinegar, and 216 mL of the 12% vinegar.