Vincent bought some files at $3 each. He later sold them to his customers at $8 each. For customers who bought three files were given another file for free. The customers bought either one or three files. Vincent gave away 130 free files and collected a total of $1610 more than what he had paid for. How many customers bought just one file each?

	Files sold	Files given to customers who got 1 file each	Files given to customers who got 4 files each
Number	1 u	1 u - 520	520
Value	$3	$8	$8
Total Value	3 u	8 u - $4160	$3120

Since 130 files were given free, there were 130 customers who bought three files each.

Number of files that each customer would get if they bought three files each and got 1 file free
= 3 + 1
= 4

Total number of files for customers who each bought three files 
= 4 x 130
= 520

Number of files for customers who each bought 1 file = 1 u - 520

Total amount collected from customers who bought 1 file each
= 8 x (1 u - 520)
= 8 u - 4160

Total amount collected from customers who bought three files each
= 130 x 3 x 8
= $3120

Total amount collected from all the customers
= 8 u - 4160 + 3120
= 8 u - 1040

Vincent collected a total of $1610 more than what he had paid for.

8 u - 1040 = 3 u + 1610
8 u - 3 u = 1610 + 1040
5 u = 2650

1 u = 2650 ÷ 5 = 530

Number of customers who bought just one file
= 1 u - 520
= 530 - 520
= 10

Answer(s): 10