Final answer:
Sarah decorated 55 dresses and sold each for $106, leading to a total collection of $5830 from the sales.
Step-by-step explanation:
The question asks us to calculate the total amount Sarah collected from the sale of the dresses. To find out how many dresses Sarah decorated, we need to determine how much lace she used in total and then calculate the number of dresses from there. Since Sarah had 730 meters of lace initially and 510 meters left after decorating the dresses, she used 730 - 510 = 220 meters of lace. As each dress requires 4 meters of lace, the number of dresses she decorated is 220 meters / 4 meters per dress = 55 dresses.
Since each dress was sold for $106, to calculate the total amount collected from the sale, we multiply the number of dresses by the sale price per dress. Therefore, the total amount Sarah collected is 55 dresses × $106 per dress = $5830.