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

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CEO
Joined: 12 Sep 2015
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Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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28 Apr 2018, 08:13
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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

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

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08 May 2018, 21:28
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.

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

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19 Aug 2018, 22:11
Hi Bunuel
I am not able to find such type of questions.

Thanks
Intern
Joined: 19 Sep 2018
Posts: 3
Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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22 Sep 2018, 23:18
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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Joined: 31 Mar 2017
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Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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13 Dec 2018, 19:28
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.

Hi,

Is this alligation rule method?

Regrds,
Rrsnathan.

Alligation

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

Posted from my mobile device
SVP
Joined: 26 Mar 2013
Posts: 2229
Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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14 Jan 2019, 05:46
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 gasohol = G & Ethanol = E

Using Alligation method

G...........M......................E
5...5 .....10.......90.........100

G/E = 90/5= 18/1 ....then

20/E = 18/1......E = 20/8 =10/9

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

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14 Jan 2019, 11:20
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

$$\frac{Ethnol}{Gasoline} = \frac{1}{19}$$

Or,$$\frac{Ethnol}{Gashol}= \frac{1}{20}$$

Or,$$\frac{1 + x}{20 + x} = \frac{10}{100}$$

Or, $$10 + 10x = 20 + x$$

Or, $$9x = 10$$

So, $$x = \frac{10}{9}$$ , thus Answer must be (C) $$\frac{10}{9}$$
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Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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22 Jan 2019, 16:50
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

My reasoning if it helps anyone:

We have one mixture that is 5% ethanol and another that is 100% ethanol. We want to mix those together to get a mixture that is 10% ethanol.

As such we need to mix them in a ratio of 18 parts gasohol to 1 part pure ethanol.

From here we can solve for the amount of ethanol that must be added:

$$\frac{18}{1} = \frac{20}{x}$$

$$x= \frac{10}{9}$$
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Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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12 Mar 2019, 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

Intern
Joined: 22 Jan 2017
Posts: 5
Re: Bob just filled his car's gas tank with 20 gallons of  [#permalink]

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29 May 2019, 05:20
Easy way to solve this (for me) was:

Given Mixture

Ethanol Gasoline Total quantity (Gallons)
1 19 20 (5% of 20 =1 and 95% of 20 = 19)

Needed some quantity to make Optimum Gasoline (10% of E and 90% Gasoline) = X

Hence,

Ethanol Gasoline Total quantity (Gallons)
1+X 19 20+X

= 10% of (20+X) = (1+X)
= 10/100*(20+X) = (1+X)
= (20+x) = 10*(1+X)
= 20+X = 10+10X
=20-10=10X-X
=10 =9X
X =10/9

Re: Bob just filled his car's gas tank with 20 gallons of   [#permalink] 29 May 2019, 05:20

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