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At Store T, the dollar amount of sales for 2007 was what per

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At Store T, the dollar amount of sales for 2007 was what per [#permalink] New post 12 Sep 2017, 14:09
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62% (01:18) correct 37% (02:17) wrong based on 86 sessions


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At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008 ?

Give your answer to the nearest 0.1 percent.

[Reveal] Spoiler: OA
108.7 %


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Question: 2
Page: 127
Difficulty: medium


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Re: At Store T, the dollar amount of sales for 2007 was what per [#permalink] New post 12 Sep 2017, 23:43
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Explanation

If A is the dollar amount of sales at Store T for 2007, then 8 percent of A, or is the amount of decrease from 2007 to 2008. Thus is 0.08A, A − 0.08A = 0.92A the dollar amount for 2008. Therefore, the desired percent can be obtained by dividing A by 0.92A which is \(\frac{A}{0.92A}\) = \(\frac{1}{0.92}\) = \(1.08 %\) = \(108.7 %\)
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Re: At Store T, the dollar amount of sales for 2007 was what per [#permalink] New post 09 Feb 2020, 04:23
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Expert's post
Notice that we don't need to know anything about the 2006 sales figures here.

All we need to know is that from 2007 to 2008, the sales DECREASED 8%
So, let's PLUG IN some nice values for 2007 and 2008 that meet this condition.

How about:
In 2007, total sales = $100
In 2008, total sales = $92
As you can see, these figures show an 8% decrease from 2007 to 2008

Question: The dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008?
In other words, $100 is what percent of $92?
In other words, express 100/92 as a percent.

Well, 100/92 = 1.08695...
This equals 108.7% (rounded to the nearest tenth of a percent)


Answer:
[Reveal] Spoiler:
108.7%


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Re: At Store T, the dollar amount of sales for 2007 was what per [#permalink] New post 09 Feb 2020, 10:44
Expert's post
The table tells us that the sales at store T DECREASED by 8% from 2007 to 2008.
So, if A = the sales from 2007...
...then the sales from 2008 = A - 8% 0f A
= A - 0.08A
= 1A - 0.08A
= 0.92A

The question asks "The dollar amount of sales for 2007 is what % of the dollar amount of sales for 2008?"
In other words, "A is what % of 0.92A?"

Let x = the unknown percent
So, we get: A = (x/100)(0.92A)
Divide both sides by 0.92A to get: A/0.92A = x/100
Simplify left side to get: 1/0.92 = x/100
Multiply both sides by 100 to get: 100/0.92 = x
Evaluate: x = 108.69%
Round to nearest 0.1% to get: 108.7%

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Brent
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Re: At Store T, the dollar amount of sales for 2007 was what per [#permalink] New post 09 Feb 2020, 10:50
Expert's post
Explanation

If A is the dollar amount of sales at Store T for 2007, then 8 percent of A, or 0.08A is the amount of decrease from 2007 to 2008.

Thus \(A - 0.08A = 0.92A\) is the dollar amount for 2008.

Therefore, the desired percent can be obtained by dividing A by 0.92A which equals The \(\frac{A}{0.92A}\), which equals \(\frac{1}{0.92}\), which equals 1.0869565...

Expressed as a percent and rounded to the nearest 0.1 percent, this number is 108.7%.

Thus, the correct answer is 108.7% (or equivalent).
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