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Question 896994: percent gain on selling the articles for 84$ is twice as much as when it is sold for $72.Find the cost of the articles.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! cost of the articles is x.
they sell for 72 and they sell for 84.
the gain on selling for 72 is 72 - x.
the gain on selling for 84 is 84 - x.
if the percent gain is double, then the gain is double.
conversely, if the gain is double, then the percent gain is double.
example:
cost is 100 and gain is 10.
percent gain is 10/100 * 100 = 10%.
cost is 100 and gain is 20.
percent gain is 20/100 * 100 = 20%.
double the gain gets double the percent gain.
back to your problem.
the gain on selling for 72 is 72 - x.
the gain on selling for 84 is 84 - x.
since the gain from selling at 84 is double the gain from selling at 72, you get the following formula:
(84 - x) = 2 * (72 - x)
you want to solve for x in this formula which will tell you what the cost of the articles was.
simplify to get 84 - x = 144 - 2x
add 2x to both sides of this equation and subtract 84 from both sides of this equation to get:
2x - x = 144 - 84
simplify to get:
x = 60
that's the cost of the articles.
when you sell at 84, your gain is 84 - 60 = 24 which is equal to 24/60 * 100 = 40% gain.
when you sell at 72, your gain is 72 - 60 = 12 which is equal to 12/60 * 100 = 20% gain.
the percent gain at 84 is double the percent gain at 72.
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