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A rainstorm increased the amount of water stored in State J [#permalink]

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16 Apr 2008, 13:28

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A

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E

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33% (02:18) wrong based on 353 sessions

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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?

Re: A rainstorm increased the amount of water stored in State J [#permalink]

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16 Apr 2008, 17:45

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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.

Re: A rainstorm increased the amount of water stored in State J [#permalink]

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01 May 2009, 04:26

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

Re: A rainstorm increased the amount of water stored in State J [#permalink]

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03 May 2009, 01:34

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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?

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.

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.