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.
