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*0.12=0.12x`

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

`10*0.04=0.4`

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

`(10+x)*0.10=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=(0.6)/(0.02) \\ x=30 \end{gathered}`

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