Rael bought some files at $2 each. He later sold them to his customers at $7 each. For customers who bought three files were given another file for free. The customers bought either one or three files. Rael gave away 110 free files and collected a total of $1930 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 - 440	440
Value	$2	$7	$7
Total Value	2 u	7 u - $3080	$2310

Since 110 files were given free, there were 110 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 110
= 440

Number of files for customers who each bought 1 file = 1 u - 440

Total amount collected from customers who bought 1 file each
= 7 x (1 u - 440)
= 7 u - 3080

Total amount collected from customers who bought three files each
= 110 x 3 x 7
= $2310

Total amount collected from all the customers
= 7 u - 3080 + 2310
= 7 u - 770

Rael collected a total of $1930 more than what he had paid for.

7 u - 770 = 2 u + 1930
7 u - 2 u = 1930 + 770
5 u = 2700

1 u = 2700 ÷ 5 = 540

Number of customers who bought just one file
= 1 u - 440
= 540 - 440
= 100

Answer(s): 100