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

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CEO
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Joined: 11 Sep 2015
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Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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New post 28 Apr 2018, 07:13
1
Top Contributor
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


Bob just filled his car's tank with 20 gallons of gasohol, a mixture containing of 5% ethanol and 95% gasoline.
5% of 20 gallons is 1 gallon.
So, PRESENTLY, there is 1 gallon of ethanol in the car's tank.


We want to add some PURE ethanol to the tank in order to get a 10% mixture of ethanol.
Let x = number of gallons of pure ethanol we ADD to the tank.

FACT #1: Once we add x more gallons of pure ethanol, the car's tank contains 1+x gallons of ethanol.

FACT #2: Once we add x gallons of ethanol, the car's tank contains a TOTAL of 20+x gallons of mixture.

We want the tank to have a 10% mixture of ethanol. In other words, we want the mixture in the tank to contain 1/10 ethanol.
So, we can write the equation: (1+x)/(20+x) = 1/10
Cross multiply to get: 10(1 + x) = 1(20 + x)
Expand: 10 + 10x = 20 + x
Rearrange: 9x = 10
Divide both sides by 9 to get: x = 10/9

Answer: C

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

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New post 08 May 2018, 20:28
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


5% of 20= 1g of ethanol


1+x = 10%(20+x), simplifying we get 10+10x=20+x => x = 10/9.

Hence answer C.

-----------------------------------------
+1 for kudos please
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Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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New post 19 Aug 2018, 21:11
Hi Bunuel
I am not able to find such type of questions.
Can you please provide links of more such questions for practice?

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

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New post 22 Sep 2018, 22:18
1
Current,
Ethanol= 20*.05=1
Gasoline= 20*.95=19
Let, x gallons of Ethanol to be mixed.
Therefore,
(1+x)/19=10/90
(1+x/19=1/9
x=10/9
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Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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New post 13 Dec 2018, 18:28
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.


Alligation

5----- 1000
---10---
90 : 5
18 : 1

Posted from my mobile device
GMAT Club Bot
Re: Bob just filled his car's gas tank with 20 gallons of &nbs [#permalink] 13 Dec 2018, 18:28

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