How many gallons each of 25% alcohol and 10% alcohol should be mixed to obtain 15 gal of 23% alcohol

Question

How many gallons each of 25% alcohol and 10% alcohol should be mixed to obtain 15 gal of 23% alcohol

Answer 1

Let A₁ = number of gallons of the 25% solution

A₂ = number of gallons of the 10% solution

Then A₁ + A₂ = 15 and using a weighted average, we have (25A₁ + 10A₂)/(A₁ + A₂) = 23

The weighted average becomes 25A₁ + 10A₂ = 15(23) = 345 so,

A₁ + A₂ = 15

25A₁ + 10A₂ = 345 Solving the two equations simultaneously, we find that

A₁ = 13 gallons of the 25% alcohol and A₂ = 2 gallons of 10% alcohol