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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]

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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

Last edited by nk9285 on 02 Jan 2013, 12:18, edited 1 time in total.
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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20 May 2013, 15:17
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]

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05 Aug 2013, 22:54
Expert's post
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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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 30 May 2013 Posts: 188 Location: India Concentration: Entrepreneurship, General Management GPA: 3.82 Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] ### Show Tags 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) Hi, Is this alligation rule method? Regrds, Rrsnathan. Senior Manager Joined: 10 Jul 2013 Posts: 334 Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] ### Show Tags 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) _________________ Asif vai..... Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7449 Location: Pune, India Re: Bob just filled his car's gas tank with 20 gallons of [#permalink] ### Show Tags 15 Aug 2013, 22:42 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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

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01 Dec 2014, 18:08
initial 20 = 1E + 19G

new 20+E = (20+E)/10 +19 (as amount of G same only E added)

=> 18 +9E/10 = 19

HENCE E = 10/9
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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02 Dec 2014, 02:46
Ethanol ............... Gasoline .............. Total

1 ............................. 19 ..................... 20 (Current fill)

1+x ........................... 19 ................... 20+x (Say "x" litres of ethanol is added to make it 10%)

Equation can be setup in two ways

$$\frac{10}{100} (20+x) = 1+x$$

OR

$$\frac{90}{100} (20+x) = 19$$

For both, computation of x would be the same

$$x = \frac{10}{9}$$

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

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

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14 Dec 2014, 04:15
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I solved it using algebra, for concepts sake, is it possible to use alligation or the scale method here?

In this post above: bob-just-filled-his-car-s-gas-tank-with-20-gallons-of-45790-20.html#p1253824
I have already shown how to use scale method here.
For more on the formula, check: http://www.veritasprep.com/blog/2011/03 ... -averages/
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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.

=> (1 + $$x$$) = $$\frac{10}{100}$$$$*(20+x)$$
=> 100 + 100$$x$$ = 200 + 10$$x$$
=> 90$$x$$ = 100
=> $$x$$ =$$\frac{10}{9}$$

Therefore, $$\frac{10}{9}$$ would be the amount of ethanol that needs to be added to $$20gl$$ of fuel.

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

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21 Aug 2015, 19:49
I solved it a different way. It took me about 3 mins so I think I might be adding an extra step but this is what worked for me.

I started by solving how many gallons of ethanol and gas are in the tank already. .05 * 20=1 (gal of e); .95 * 20=19 (gal of g)

The current ratio of e:g is 1/19. The ideal ratio is 10/90 or 1/9. This question asks how much more ethanol we need to get to the 1/9 ratio.

Thus, e/19 = 1/9. --> 9e=19. e=19/9 total. As there is already 1 gal of e in there, 19/9 - (9/9)= 10/9 more gal of e.
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Bob just filled his car's gas tank with 20 gallons of [#permalink]

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23 May 2016, 21:22
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

E:G
5%:95% >> 1:19

19 is 90% of 190/9. 10% of 190/9 is 19/9.
so we need : 19/9-9/9 = 10/9 gallons more.
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Re: Bob just filled his car's gas tank with 20 gallons of [#permalink]

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24 May 2016, 06:34
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 x gallon ethanol is added, making the total solution= 20+x

5% of 20 + x = 10%(20+x)
1+x= 2 + x/10
x-x/10= 1
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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23 May 2017, 21:01
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

This problem involves weighted averages, but there isn't a shortcut per-se. Instead, you should take the the current amount (1 gallon) plus x, the incremental amount of gas, and set this quantity equal to (x+20)/10, a tenth of the new total once the incremental gas has been added. This righthand quantity is the ideal amount.

After this point, it's easy algebra to determine that 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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26 May 2017, 11:47
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

We can let x = the number of gallons of ethanol to be added to the gas tank.

Note that since the 20-gallon mixture of gasohol is 5% ethanol, there is 20 x 0.05 = 1 gallon of ethanol already in the tank. Since we want the gasohol to be 10% ethanol, we have the following equation:

(1 + x)/(20 + x) = 10/100

(1 + x)/(20 + x) = 1/10

10(1 + x) = 20 + x

10 + 10x = 20 + x

9x = 10

x = 10/9

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Re: Bob just filled his car's gas tank with 20 gallons of   [#permalink] 26 May 2017, 11:47

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