Question

A sugar solution was made by mixing 3 gal. of a 50% sugar solution and 9 gal. of a 30% sugar solution. Find the concentration of the new mixture.

Answer 1

The new mixture is acquired from the sum of the concentration divided by the total number of gallons. Or we could write it like this.
mix = $\cfrac{\text{concentrate} \times gallons+\text{concentrate} \times gallons}{\text{the total number of gallons}}$

Input the numbers
mix = $\cfrac{50 \% \times 3+30 \% \times 9}{3+9}$

simplify the dividend and divisor
mix = $\cfrac{150 \%+270 \%}{12}$
mix = $\cfrac{420 \%}{12}$
mix = $\cfrac{420 \%}{12}$
mix = 35%

The new concentration is 35%