Final answer:
Daniel received $147 of the money. The solution was found by determining the value of each part in the ratio 3:5:9 given that the difference between the shares of Gabriel and Hadley is $196.
Step-by-step explanation:
Daniel, Gabriel, and Hadley share money in the ratio of 3:5:9, and the difference in the amount received by Gabriel and Hadley is $196. To find out how much Daniel receives, first, we recognize that the difference between Gabriel and Hadley's shares corresponds to 4 parts of the ratio (9 parts - 5 parts = 4 parts). Since 4 parts are equivalent to $196, 1 part is equal to $196 divided by 4, which equals $49. Next, calculate the total number of parts in the ratio which is 3 parts + 5 parts + 9 parts = 17 parts. With 1 part equaling $49, the total amount of money shared is 17 parts times $49, which equals $833. Daniel's share is 3 parts of the ratio, so Daniel receives 3 parts times $49, which equals $147. Therefore, Daniel received $147.