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A rainstorm increased the amount of water stored in State J

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A rainstorm increased the amount of water stored in State J [#permalink] New post 16 Apr 2008, 12:28
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A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-rainstorm-increased-the-amount-of-water-stored-in-state-j-136559.html
[Reveal] Spoiler: OA
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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 16 Apr 2008, 12:55
Let total capacity be x

we know 138 = 0.82x
x = 138/0.82 = 168.29

Prior to storm, we had 124 bn gallons

168-124 = 44

Answer is E
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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 16 Apr 2008, 16:45
Thanks for the reply, yellowjacket.

I feel kind of dumb now with the answer being so simple, but constructing equations from word problems is a really weak point of mine. I tend to get confused about which is the variable.
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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 17 Apr 2008, 07:30
yellowjacket wrote:
x = 138/0.82 = 168.29


That math is such a pain without a calculator.... :lol:
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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 01 May 2009, 03:26
well the answer is E 44
just ask yourself 82% of what is 138
to find out that it is 168.3 which is the total capacity
but they asked what was the amount prior to the storm which is 168-124 = 44
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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 03 May 2009, 00:34
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

[Reveal] Spoiler: Explanation
OG:
Let t be the total capacity of the reservoirs in billions of gallons. The information that the post-storm water amount of 138 billion gallons represented 82 percent of total capacity can be expressed as 0.82t = 138. Solve for t and then estimate the value of t:
\(t = \frac{138}{0.82} \approx \frac{140}{0.8} = \frac{1400}{8} = 175\) billion gallons. Thus, the amount the reservoirs were short of total capacity prior to the storm, in billions of gallons, was approximately 175 - 124 = 51, so E is the best choice. A more accurate calculation gives 168.3 - 124 = 44.3.

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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 13 Feb 2011, 10:06
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Amount after rainstorm = 138 billion
Total capacity = C billion

Given: 82/100 x C = 138 or C = 138/82 x 100

Question: C - 124 = ?

138/82 x 100 - 124 = ?

(13800 - 124 x 82)/82 = 44 (aprox)
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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 18 Jul 2014, 18:31
Any algebraic or factorization trick to get the 138/0.82 part?
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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 18 Jul 2014, 22:16
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Enael wrote:
Any algebraic or factorization trick to get the 138/0.82 part?


138/0.82 = 13800/82 = (138/82)*100
ignore 100, calculate: 138/82 = 69/41 = 1.683
multiply 1.683 with 100 = 168.3

I hope it helps a little bit :)
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Re: A rainstorm increased the amount of water stored in State J [#permalink] New post 19 Jul 2014, 02:46
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A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

Since we need to find only an approximate value and the answer choices are quite widespread, then use:

80% instead of 82% (notice that this approximation gives the bigger tank capacity);
140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity);
130 billion gallons instead of 124 billion gallons;.

Notice that the third approximation balances the first two a little bit.

So, we'll have that: \(capacity*0.8=140\) --> \(capacity=\frac{140}{0.8}=175\).

Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175-130=45\) billion gallons.

Answer: E.

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Re: A rainstorm increased the amount of water stored in State J   [#permalink] 19 Jul 2014, 02:46
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