Question

Find the number of gallons of a 50% alcohol solution, x, that should be mixed with 10 gallons of a 35% solution in order to get a 40% solution.

Answer 1

`\boxed{\text{5 gal}}`

Step-by-step explanation:

The volume of pure alcohol is constant.

The total volume after mixing is (x + 10) gal.

`\begin{array}{rcl}\text{Vol. alcohol in 50 \% + Vol. alcohol in 35 \%} & = & \text{Vol. alcohol in 40 \%}\\c_(1)V_(1) + C_(2)V_(2)&=& c_(3)V_(3)\\50x + 35 * 10 & = & 40(x+10)\\50x + 350 & = & 40x + 400\\10x + 350 & = & 400\\10x & = & 50\\x & = & \mathbf{5}\\\end{array}\\\text{You must mix $\boxed{\textbf{5 gal}}$ of 50 \% alcohol with 10 gal of 35\% alcohol.}`

Check:

`\begin{array}{rcl}50 * 5 + 35 * 10 & = & 40(5 + 10)\\250 + 350 & = & 40 * 15\\600 & = & 600\\\end{array}`