Question

How many gallons of 12% ethanol solution is needed to produce a 10% ethanol solution

Answer 1

We are asked to determine how much of a 12% ethanol fuel mixture should be mixed with 10 gallons of 4% ethanol fuel mixture to get a mixture that is 10% ethanol.

Let x be the required number of gallons of ethanol mixture.

The amount of ethanol fuel mixture in x gallons of solution with 12% ethanol fuel mixture is given by

$x\times0.12=0.12x$

The amount of ethanol fuel mixture in 10 gallons of solution with 4% ethanol fuel mixture is given by

$10\times0.04=0.4$

The amount of ethanol fuel mixture in (10+x) gallons of solution with 10% ethanol fuel mixture is given by

$(10+x)\times0.10=1+0.10x$

So, the equation becomes

$0.12x+0.4=1+0.10x$

Let us solve the above equation for x.

$\begin{gathered} 0.12x+0.4=1+0.10x \\ 0.12x-0.10x=1-0.4 \\ 0.02x=0.6 \\ x=\frac{0.6}{0.02} \\ x=30 \end{gathered}$

30 gal of 12% ethanol solution is needed to produce a 10% ethanol solution.