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
We can let x = the number of gallons of ethanol to be added to the gas tank.
Note that since the 20-gallon mixture of gasohol is 5% ethanol, there is 20 x 0.05 = 1 gallon of ethanol already in the tank. Since we want the gasohol to be 10% ethanol, we have the following equation:
(1 + x)/(20 + x) = 10/100
(1 + x)/(20 + x) = 1/10
10(1 + x) = 20 + x
10 + 10x = 20 + x
9x = 10
x = 10/9
Answer: C
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