Alex, Tom and Edward started a business by investing $800, $1600 and \$2000, respectively. After a quarter, they invested more in the ratio 1 : 4 : 2. After another quarter, they invested more in the ratio 3 : 2 : 3. In the last quarter, the ratio of investments was same as in the 2nd quarter. Also, in the last quarter, the respective amounts of Alex, Tom and Edward were double the respective amounts invested in the 2nd quarter. The total investment of Edward before the 4th quarter was \$1400 more than that of Alex during the same duration. Also, the ratio of Tom's share in the profit to the total profit at the end of the year was 22 : 51. Find the total investment of all three.
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