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

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

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

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

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

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

Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]
19 Sep 2014, 07:56

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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]
19 Nov 2014, 04:17

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]
11 Dec 2014, 06:40

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?

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