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Bob just filled his car's gas tank with 20 gallons of

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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] New post 02 Jan 2013, 11:01
In the original mixture we have 95% G= 19 gallons and 5% E= 1 gallon
We have to add X amount of Ethanol to make it 90:10 mixture,
hence:
(1+x/20+x)*100=10
(1+x)*10=20+x
9x=10; x=10/9
thus the answer is C

Last edited by nk9285 on 02 Jan 2013, 11:18, edited 1 time in total.
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] New post 20 May 2013, 14:17
I got 1 cause i got 5% to be 1 and the reason i forgot that is because i forgot to 95% gasoline
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] New post 05 Aug 2013, 21:54
Expert's post
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



Responding to a pm:

Using Weighted average formula:

w1/w2 = (A2 - Avg)/(Avg - A1)

You need to mix 5% ethanol mixture with 100% ethanol to give a 10% ethanol mixture.

w1/w2 = (100 - 10)/(10 - 5) = 18/1

For every 18 parts of gasohol, you need to put 1 part of pure ethanol.
So if you have 20 gallons of gasohol, you need to put 20/18 (= 10/9) gallons of pure ethanol.
Answer (C)
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] New post 14 Aug 2013, 04:49
VeritasPrepKarishma wrote:
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



Responding to a pm:

Using Weighted average formula:

w1/w2 = (A2 - Avg)/(Avg - A1)

You need to mix 5% ethanol mixture with 100% ethanol to give a 10% ethanol mixture.

w1/w2 = (100 - 10)/(10 - 5) = 18/1

For every 18 parts of gasohol, you need to put 1 part of pure ethanol.
So if you have 20 gallons of gasohol, you need to put 20/18 (= 10/9) gallons of pure ethanol.
Answer (C)


Hi,

Is this alligation rule method?

Regrds,
Rrsnathan.
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] New post 15 Aug 2013, 03:38
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

Ethanol now = 5% of 20 = 1 gallon
Let, we need x gallons of ethanol .

so, (20+x)/(1+x) = 100/10 or, x = 10/9 (Answer)
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] New post 15 Aug 2013, 21:42
Expert's post
rrsnathan wrote:
VeritasPrepKarishma wrote:
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



Responding to a pm:

Using Weighted average formula:

w1/w2 = (A2 - Avg)/(Avg - A1)

You need to mix 5% ethanol mixture with 100% ethanol to give a 10% ethanol mixture.

w1/w2 = (100 - 10)/(10 - 5) = 18/1

For every 18 parts of gasohol, you need to put 1 part of pure ethanol.
So if you have 20 gallons of gasohol, you need to put 20/18 (= 10/9) gallons of pure ethanol.
Answer (C)


Hi,

Is this alligation rule method?

Regrds,
Rrsnathan.


Yes, alligation uses a diagram (with a cross with average in the middle) which leads to this formula. This formula is very effective in solving most weighted average/mixture problems.
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] New post 19 Sep 2013, 03:50
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


Let the total gallons = 100.
therefore, it has 5 gallon ethanol and 95 gallon gasoline and we need to make the mixture of 10:90 instead.
Let the volume of ethanol added be 'x' in order to make the ratio 10:90.
therefore, (5+x)/95 = 10/90.
x = 50/9.

Now, if in 100 gallons of fuel we need to add, 50/9 gallons of ethanol to make the ratio 10:90
In 20 gallons we would add = (50/9)/100 X 20 (simple unitary method)
= 10/9 (Ans)
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] New post 19 Sep 2014, 07:56
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Re: Bob just filled his car's gas tank with 20 gallons of   [#permalink] 19 Sep 2014, 07:56
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