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Trouble with percentage increase

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Trouble with percentage increase

by ellexay » Thu Feb 12, 2009 6:37 am
Year 93 Revenue: 6 (billions of dollars)
Year 94 Revenue: 8 (billions of dollars)
Year 95 Revenue: 10 (billions of dollars)
Year 96 Revenue: 11.3 (billions of dollars)


The graph above shows the combine revenue , in billions of dollars, of a chain of food stores for each year over a 4-year period. In 94, a certain stores' revenue accounted for 2% of the combined revenue for that year, and in 95, the same store accounted for 2.3% of the combined revenue for that year. What was the approximate % increase in revenue for this store from 94 to 95?

A. 0.3%
B. 15%
C. 25%
D.30.4%
E.43.8%

Ans. E

Help! THank you all.
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by DanaJ » Thu Feb 12, 2009 7:13 am
Well, let's put those word into equations. Notations first:
x = certain store's revenue in 94
y = certain store's revenue in 95.

What you should notice is that 8 is 4/3 of 6, meaning that the percentage increase of total revenue is 33.33% or that 8 = 1,33*6.
Then you get that 2% of 6 is x, meaning that x = 0.02*6 = 0.12.
You also get that 2.3% of 8 is y, giving us y = 0.023 * 1.33 * 6. Since 0.023 = 0.02 + 0.003, then this last equation can be split into 0.02*1.33*6 + 0.003*1.33*6. Now, since we've already established that 1.33*6 = 8, then we get that 0.003*1.33*6 = 0.003*8 = 0.024.
This means that y = 0.02*1.33*6 + 0.024.
You can also notice two things:
a. 0.02*1.33*6 = 0.02*6*1.33 = x * 1.33
b. 0.024 = 0.1*0.24 = 0.1*x
This makes y = 1.33x + 0.1x = 1.43x, so y is 43% greater than x.

But maybe there's an easier way around this one...
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Re: Trouble with percentage increase

by yangliu0401 » Thu Feb 12, 2009 7:17 am
ellexay wrote:Year 93 Revenue: 6 (billions of dollars)
Year 94 Revenue: 8 (billions of dollars)
Year 95 Revenue: 10 (billions of dollars)
Year 96 Revenue: 11.3 (billions of dollars)


The graph above shows the combine revenue , in billions of dollars, of a chain of food stores for each year over a 4-year period. In 94, a certain stores' revenue accounted for 2% of the combined revenue for that year, and in 95, the same store accounted for 2.3% of the combined revenue for that year. What was the approximate % increase in revenue for this store from 94 to 95?

A. 0.3%
B. 15%
C. 25%
D.30.4%
E.43.8%

Ans. E

Help! THank you all.

In 1994, the certain store's revenue was 8*2%=0.16
In 1995, the certain store's revenue was 10*2.3%=0.23
Then, the increase from 1994 to 1995= 0.23-0.16=0.07
So the increased percentage=0.07/0.16=43.8%

Pls remember, when calculating the increased percentage, you must use the number before the increase as the denominator. :)
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by ellexay » Thu Feb 12, 2009 7:18 am
Thank you, Dana, the helpful explanation! I am wondering whether there is an easier way around this as well though. Maybe a way to eyeball it?
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by ellexay » Thu Feb 12, 2009 7:22 am
Yangliu, that was wonderful. Thanks!
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by mcdesty » Sat Oct 13, 2012 2:19 am
[[2.3(10)/2(8)] - 1]* 100
3.5/8..If it were 4 in the numerator we would have 50%..We want an answer just a little bit under 4..Only E does!
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