Question

Suppose a fuel mixture is 7% ethanol and 93% gasoline. How much ethanol (in gallons) must you add to one gallon of the fuel so that the new fuel mixture is 10% ethanol?

Answer 1

\[.07+x=.10(1+x)\]

Answer 2

you have one gallon to begin with, which is 7% ethanol, so it has .07 of a gallon of ethanol. if you add x amount of ethanol you will have .07 + x amount of ethanol and
\[1+x\] amount of mixture. you want this to be 10% ethanol, so you want
\[.07+x=.10(1+x)\]

Answer 3

easier to solve if you write
\[7+100x=10(1+x)\] i.e. multiply everything by 100
then you get
\[7+100x=10+10x\]
\[90x=3\]
\[x=\frac{3}{90}=\frac{1}{30}\]