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Question 1109314: Susan Marciano invested part of her $39,000 bonus in a fund that paid an 11% profit and invested the rest in stock that suffered a 4% loss. Find the amount of each investment if her overall net profit was $2,790.
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
The traditional algebraic approach to this kind of problem is to say 11% of one amount -4% of another amount equals $2790, where the sum of the two amounts is $39,000.
Let x = amount invested in the fund
Then (39000-x) = amount invested in the stock
She invested x = $29,000 in the fund and (39000-x) = $10,000 in the stock.
Here is a way to solve this kind of problem that I find much faster....
Determine how much profit she would have had if she had invested all the money in the fund, and determine how much loss she would have had if she had invested it all in the stock. Where the actual profit of 2790 lies between those two numbers determines the ratio in which the money was split between the two investments.
Here is a diagram that makes this method easy to use:
The numbers in the first column are what the results would have been if all the money had been invested in one place or the other; the number in the middle column is her actual profit.
The numbers in the third column are the differences, calculated diagonally, between the numbers in the first and second second columns: 4290-2790 = 1500; 2790-(-1560) = 4350.
Those numbers in the third column show the ratio in which the money must be split: 4350:1500 = 29:10.
$39,000 split in the ratio 29:10 means $29,000 in the fund and $10,000 in the stock.
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