How many ounces of a 17% alcohol solution and a 34% alcohol solution must be combined to obtain 51 ounces of a 32% solution?

Answer is: 6 ounces of a 17% alcohol solution and 45 ounces of a 34% alcohol solution.

ω₁ = 17% ÷ 100% = 0.17.

ω₂ = 34% ÷ 100% = 0.34.

ω₃ = 32% ÷ 100% = 0.32.

V₁ = ?; volume of 17% antifreeze.

V₂ = ?; volume of 34% antifreeze.

V₃ = V₁ + V₂.

V₃ = 51 oz.

V₁ = 51 oz - V₂.

ω₁ · V₁ + ω₂ ·V₂ = ω₃ · V₃.

0.17 · (51 oz - V₂) + 0.34 · V₂ = 0.32 · 51 oz.

8.67 oz - 0.17V₂ + 0.34V₂ = 16.32 oz.

0.17V₂ = 7.65 oz.

V₂ = 7.65 oz ÷ 0.17.

V₂ = 45 oz.

V₁ = 51 oz - 45 oz.

V₁ = 6 oz.

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