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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