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F is going to use a mixture of two brands of italian dressing. the first brand contains 9% vinegar, and the second brand contains 14% vinegar. the chef wants to make 380 milliliters of a dressing that is 12% vinegar. how much of each brand should she use?

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Dejanras

Answer is: 152 mL of 9% vinegar and 228 mL of 14% vinegar.

ω₁ = 9% ÷ 100% = 0.09.
ω₂ = 14% ÷ 100% = 0.14.
ω₃ = 12% ÷ 100% = 0.12.
V₁ = ?.

V₂ = ?.
V₃ = V₁ + V₂.
V₃ = 380 mL.

V₁ = 380 mL - V₂.
ω₁ · V₁ + ω₂ ·V₂ = ω₃ · V₃.

0.09 · (380 mL - V₂) + 0.14 · V₂ = 0.12 · 380 mL.

34.2 mL - 0.09V₂ + 0.14V₂ = 45.6 mL.

0.05V₂ = 11.4 mL.

V₂ = 11.4 mL ÷ 0.05.

V₂ = 228 mL.

V₁ = 380 mL - 228 mL.

V₁ = 152 mL.

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