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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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02 Jan 2013, 12:01

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, 12:18, edited 1 time in total.

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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05 Aug 2013, 22:54

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) _________________

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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14 Aug 2013, 05:49

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)

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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15 Aug 2013, 04:38

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) _________________

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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15 Aug 2013, 22:42

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. _________________

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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19 Sep 2013, 04:50

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)

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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19 Sep 2014, 08:56

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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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19 Nov 2014, 05:17

Let x is the gallons of ethanol to be added in the mixture => x has 100% ethanol. Totally ignore the information about gasoline because we're dealing with ethanol now.

The new mixture should be 20 + x (gallons) and have 10% ethanol => (20+x)*10% Add x gallons of 100% ethanol to 20 gallons of 5% ethanol => x*100% + 20*5% = x+1

We have the equation: (20 + x)*0,1 = x + 1 => x = 10/9

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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11 Dec 2014, 07:40

VeritasPrepKarishma wrote:

Emaco wrote:

Guys, I made the following formula, could anyone of you please tell me what's wrong with it ? 0.95 (20) + X = 90/100 (20+x) 1+X = 18+0.9x 0.1x = 17 ???

.95 of 20 is the amount of gasoline already in his car. He adds more ethanol and not gasoline so you cannot add x (amount of ethanol added) to .95 of 20.

Instead, you need to find the current amount of ethanol and add x to it.

.05(20) + x = .10 (20 + x) .9x = 1 x = 10/9

I solved it using algebra, for concepts sake, is it possible to use alligation or the scale method here?

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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21 Aug 2015, 13:32

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

Using the cross method works out the best way to solve mixtures problems. But in this problem the final conversion from 18 parts to the asked 20 parts was something that tricked me. The silliness struck me after i solved it algebraically.

\(Soln:\) Total amount: 20 Ethanol = \(\frac{5}{100}*20=1gl\) Gasoline = \(\frac{95}{100}*20=19gl\)

Let \(x\) be the amount of ethanol that will be added to get 10% of ethanol in the final solution.

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