Question

How much of a 10% ethanol fuel mixture should be mixed with 14 gal of 5% ethanol fuel mixture to get a mixture that is 8% ethanol?

Answer 1

21 gallons.

Explanation:

First, we need to find the total gallons of ethanol in the 5% ethanol fuel mixture with a volume of 14 gallons. 5% of 14 is 0.7. This means there are 0.7 gallons of ethanol present in the mixture.

For a 10% ethanol fuel mixture, if we have an x amount of gallons of total fuel mixture, there is 10% of x, or 0.1x gallons that are just ethanol fuel.

In the end, we need to have 8% ethanol in our total mixture, meaning the volume of ethanol over volume of mixture should equal 8%, or 0.08.

We can setup an equation with this following information:

`(\left(0.7+0.1x\right))/(14+x)=0.08`

When we add two mixtures, the total volume of both mixtures add, hence the 14+x in the denominator (we are adding x gallons of 10% mixture). The total gallons of ethanol also mix, hence the 0.7 + 0.1x, as there is 0.7 gallons of ethanol in the 14 gallon mixture, and 10% of x is the ethanol in the second mixture.

Because in the end, the volume of ethanol over volume mixture should be 8% to get the desired target of 8% ethanol, this fraction should equal 8%, or 0.08. Solving the equation, we have x = 21.