Final answer:
The organizers received $3600 in registration fees from 108 organizations, which included 36 non-profit organizations and 72 for-profit organizations at an event.
Step-by-step explanation:
The question asks for the total amount of money received in registration fees from non-profit and for-profit organizations that set up booths at an event. Given that the ratio of non-profit to profit organizations is 3 to 6 and there are 108 organizations in total, we can use the ratio to calculate the number of each type of organization.
The ratio implies that for every 9 organizations (3 + 6), 3 are non-profit and 6 are for-profit. Dividing the total number of organizations (108) by the sum of the parts of the ratio (9) gives us the number of times this ratio is contained within the total: 108 / 9 = 12. Multiplying this by the parts of the ratio gives us 36 non-profit organizations (3 x 12) and 72 for-profit organizations (6 x 12).
Since the non-profit organizations paid a $20 registration fee and the for-profit organizations paid a $40 fee, we can calculate the total fees by multiplying the number of organizations of each type by the respective fee. Hence, the total fees from non-profit organizations is 36 x $20 = $720, and the total fees from for-profit organizations is 72 x $40 = $2880. Adding these two amounts gives us the total registration fees collected: $720 + $2880 = $3600.
Therefore, the organizers received $3600 in registration fees from the 108 organizations.