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 Post subject: GMAT Algebra
PostPosted: Mon Apr 08, 2013 7:38 am 
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Joined: Tue Apr 13, 2010 8:48 am
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A fish tank is half full of water. If 10 gallons of water were added, the tank would be 7/8 full. What is the capacity of the tank (in gallons)?

A. 11 3/7
B. 22 3/7
C. 26 2/3
D. 30 3/8
E. 32 1/8

(C) Set G as the capacity of the tank. Now we translate the question: half of the tank plus ten gallons equals 7/8 of the tank. This can be written out as:
G/2 + 10 = (7/8)G.

Subtract G/2 from both sides and convert G/2 into (4/8)G, in order to give both fractions a common denominator. The equation then becomes:
10 = (7/8)G – (4/8)G
(3/8)G = 10.

Multiply both sides by 8/3:
G = 10(8/3) = 80/3 = 26.66 or 26 2/3 gallons. The correct answer is choice (C).
-------------

How do you convert G/2 into 4/8?


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 Post subject: Re: GMAT Algebra
PostPosted: Mon Apr 08, 2013 7:40 am 
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We convert G/2 into (4/8)G.

G/2 = 1/2 × G = (1 × 4)/(2 × 4) × G = 4/8 × G


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 Post subject: Re: GMAT Algebra
PostPosted: Mon Apr 08, 2013 7:42 am 
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Where does 4/8 come from?


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 Post subject: Re: GMAT Algebra
PostPosted: Mon Apr 08, 2013 7:42 am 
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Joined: Fri Apr 09, 2010 2:11 pm
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We convert G/2 into (4/8)G.

G/2 is 1/2 × G and 4/8 is 1/2.

G/2 = 1/2 × G = (1 × 4)/(2 × 4) × G = 4/8 × G


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