above720 wrote:

Bob just filled his car's gas tank with 20 gallons of gasohol, a mixture consisting of 5% ethanol and 95% gasoline. If his car runs best on a mixture consisting of 10% ethanol and 90% gasoline, how many gallons of ethanol must he add into the gas tank for his car to achieve optimum 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) =

1/10Cross 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 = 10/9

Answer: C

Cheers,

Brent

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