A can do a piece of work in 4 days, while B can do the same work in 5 days. Both of them finish the work together and get $450. What is B's share (in dollars)?

Assuming the total work is 20 units, the Least Common Multiple of 4 and 5. A completes 5 units per day and B completes 4 units per day. When working together, their combined effort is 9 units per day, meaning they complete the work in 20 / 9 days. B's total work done is 4 units per day multiplied by 20 / 9 days, which equals 80 / 9 units. Since B completes (80 / 9) / 20 = 4 / 9 of the total task, he receives 4 / 9 of the $450 total payment. B's share is calculated as 450 * (4 / 9) = 200 dollars.

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