Ken bought some files at $2 each. He later sold them to his customers at $6 each. For customers who bought three files were given another file for free. The customers bought either one or three files. Ken gave away 180 free files and collected a total of $1920 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 - 720 |
720 |
Value |
$2 |
$6 |
$6 |
Total Value |
2 u |
6 u - $4320 |
$3240 |
Since 180 files were given free, there were 180 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 180
= 720
Number of files for customers who each bought 1 file = 1 u - 720
Total amount collected from customers who bought 1 file each
= 6 x (1 u - 720)
= 6 u - 4320
Total amount collected from customers who bought three files each
= 180 x 3 x 6
= $3240
Total amount collected from all the customers
= 6 u - 4320 + 3240
= 6 u - 1080
Ken collected a total of $1920 more than what he had paid for.
6 u - 1080 = 2 u + 1920
6 u - 2 u = 1920 + 1080
4 u = 3000
1 u = 3000 ÷ 4 = 750
Number of customers who bought just one file
= 1 u - 720
= 750 - 720
= 30
Answer(s): 30