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 11% vinegar. the chef wants to make 240 milliliters of a dressing that is 8% vinegar. how much of each brand should she use?

Answer 1

Answer is: 180 mL of 7% vinegar and 60 mL of 11% vinegar.

ω₁ = 7% ÷ 100% = 0.07.
ω₂ = 11% ÷ 100% = 0.11.
ω₃ = 8% ÷ 100% = 0.08.
V₁ = ?.

V₂ = ?.
V₃ = V₁ + V₂.
V₃ = 240 mL.

V₁ = 240 mL - V₂.
ω₁ · V₁ + ω₂ ·V₂ = ω₃ · V₃.

0.07 · (240 mL - V₂) + 0.11 · V₂ = 0.08 · 240 mL.

16.8 mL - 0.07V₂ + 0.11V₂ = 19.2 mL.

0.04V₂ = 2.4 mL.

V₂ = 2.4 mL ÷ 0.04.

V₂ = 60 mL.

V₁ = 240 mL - 60 mL.

V₁ = 180 mL.