safina wrote: Bob just filled his car's tank with 20 gallons of gasohol, a mixture containing of 5% ethanol and 95% gasoline. If his car runs best on a mixture containing of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimal performance?
A) 9/10
B) 1
C) 10/9
D) 20/19
E) 2

Bob just filled his car's tank with 20 gallons of gasohol, a mixture containing of 5% ethanol and 95% gasoline.
5% of 20 gallons is 1 gallon.
So, PRESENTLY, there is 1 gallon of ethanol in the car's tank.


We want to add some PURE ethanol to the tank in order to get a 10% mixture of ethanol.
Let x = number of gallons of pure ethanol we ADD to the tank.

FACT #1: Once we add x more gallons of pure ethanol, the car's tank contains 1+x gallons of ethanol.

FACT #2: Once we add x gallons of ethanol, the car's tank contains a TOTAL of 20+x gallons of mixture.

We want the tank to have a 10% mixture of ethanol. In other words, we want the mixture in the tank to contain 1/10 ethanol.
So, we can write the equation: (1+x)/(20+x) = 1/10
Cross multiply to get: 10(1 + x) = 1(20 + x)
Expand: 10 + 10x = 20 + x
Rearrange: 9x = 10
Divide both sides by 9 to get: x = [spoiler]10/9[/spoiler]

Answer: C

Cheers,
Brent