Question

A chemical company makes two brands of antifreeze. the first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. in order to obtain 140 gallons of a mixture that contains 85% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

Answer is: 56 gallons of 70% antifreeze and 84 gallons of 95% antifreeze.

ω₁ = 70% ÷ 100% = 0.7; 70% pure antifreeze.

ω₂ = 95% ÷ 100% = 0.95.

ω₃ = 85% ÷ 100% = 0.85.
V₁ = ?; volume of 70% antifreeze.

V₂ = ?; volume of 95% antifreeze.
V₃ = V₁ + V₂.
V₃ = 140 gal.

V₁ = 140 gal - V₂.
ω₁ · V₁ + ω₂ ·V₂ = ω₃ · V₃.

0.70 · (140 gal - V₂) + 0.95 · V₂ = 0.85 · 140 gal.

98 gal - 0.7V₂ + 0.95V₂ = 119 gal.

0.25V₂ = 21 gal.

V₂ = 21 gal ÷ 0.25.

V₂ = 84 gal.

V₁ = 140 gal - 84 gal.

V₁ = 56 gal.