gasoline problem

[pappueshwar]

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?


i thought the answer to be as 1 but its nt that way .request to explain


9/10

1

10/9

20/19

2

[optimist.tageja]

i think level of this question would be 640-650

1. in 20 gallons of mixture 5% is ethanol, that would be 1 gallon, and rest of 19 gallon is gasoline.
2. no we need to add ethanol so that the composition of ethanol in the mixture would become 10%.
3. considering 19 gallon of gasoline in the mixture to be 90%, we can figure out how much is the total volume of the gasohol -- x*(90/100)=19, x will come out to be 190/9.
5. now subtract 19 out of 190/9, it will be 19/9.
6. out of 19/9 gallons of ethanol 1 gallon was already there in the mixture, subtract 1 out of 19/9
19/9-1 = 10/9
and that is your answer..

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[pemdas]

0.1(20+x)=0.05*20+x, multiply both sides by 100, 200+10x=100+100x, 90x=100, x=100/90=10/9

c

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?


i thought the answer to be as 1 but its nt that way .request to explain


9/10

1

10/9

20/19

2

[LalaB]

(20*0.05+x)/(20+x)=1/10

(1+x)/(20+x)=1/10
10+10x=20+x
9x=10
x=10/9

[GMATGuruNY]

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?


i thought the answer to be as 1 but its nt that way .request to explain


9/10

1

10/9

20/19

2

Current amount of ethanol = (.05)20 = 1.

We can plug in the answers, which represent the amount of ethanol that needs to be added.
Start with the middle answer choice.
If 10/9 doesn't work, we'll be able to see whether more or less ethanol is needed.

Answer choice C: 10/9
New amount of ethanol = 1 + 10/9 = 19/9.
New total of gasohol = 20 + 10/9 = 190/9.
New ethanol/new total = (19/9) / (190/9) = 19/190 = 1/10 = 10%.
Success!

The correct answer is C.