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A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any

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A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any  [#permalink]

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New post Updated on: 23 Jul 2015, 10:38
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A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs $3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicle’s tank?

(1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles.

(2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank

Originally posted by shobuj40 on 31 Jan 2009, 11:05.
Last edited by Bunuel on 23 Jul 2015, 10:38, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to DS forum.
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Re: A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any  [#permalink]

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New post 31 Jan 2009, 14:53
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shobuj40 wrote:
A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs $3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicle’s tank?

1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles.
2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank


D.

1) 20x + 40 (8-x) = 200.
x = Fuel x and y = 8-x
x = 6
y = 2. suff.

2) 20/3 (a) + 40/5 (1-a) = 50/7

a = 9/14
1-a = 5/14

fraction of $ for fuel x + fraction of $ for fuel y = 1
a = fraction of $ for fuel x
1-a = fraction of $ for fuel y

suff...
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Re: A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any  [#permalink]

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New post 01 Feb 2009, 22:04
GMAT TIGER wrote:
shobuj40 wrote:
A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any mixture of X and Y. Fuel X costs $3 per gallon; the vehicle can go 20 miles on a gallon of Fuel X. In contrast, Fuel Y costs $5 per gallon, but the vehicle can go 40 miles on a gallon of Fuel Y. What is the cost per gallon of the fuel mixture currently in the vehicle’s tank?

1) Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles.
2) The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank


D.

1) 20x + 40 (8-x) = 200.
x = Fuel x and y = 8-x
x = 6
y = 2. suff.

2) 20/3 (a) + 40/5 (1-a) = 50/7

a = 9/14
1-a = 5/14

fraction of $ for fuel x + fraction of $ for fuel y = 1
a = fraction of $ for fuel x
1-a = fraction of $ for fuel y

suff...


I'm sorry but I don't get the 2nd equation. Can you explain why 20/3(a) = fraction of $ for fuel x?
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Re: A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any  [#permalink]

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New post 01 Feb 2009, 23:30
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Great explanation GMATTIGER!

@wcgmatclub -
For every dollar spent on Fuel X, you can travel 20/3 miles
For every dollar spent on Fuel Y, you can travel 40/5 miles

For every dollar spent on the mixture of X and Y, you can travel 7 1/7 miles. The question is asking what is the mixture?

Therefore, a(20/ 3) + (1-a)40/5 = 50/7

Cheers,
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Re: A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any  [#permalink]

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New post 13 Mar 2018, 03:05
Let there be x gallons of fuel X, and y gallons of fuel Y

question: cost per gallon? = (3x + 5y)/(x + y)
all we need is relation between x and y, or the ratio of x and y

Statement 1: Using fuel currently in its tank, the vehicle burned 8 gallons to cover 200 miles
pretty straight forward, x + y = 8, 20x + 40y = 200, two equations to find x and y => suff

Statement 2: The vehicle can cover 7 and 1/7 miles for every dollar of fuel currently in its tank
Total miles can cover / total cost = 50/7
(20x + 40y)/(3x + 5y) = 50/7 => rearranging we get, 3y = x, so we found the relation between x and y => sufficient

(D)
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Re: A certain military vehicle can run on pure Fuel X, pure Fuel Y, or any &nbs [#permalink] 13 Mar 2018, 03:05
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