Carl bought some files at $4 each. He later sold them to his customers at $6 each. For customers who bought two files were given another file for free. The customers bought either one or two files. Carl gave away 150 free files and collected a total of $180 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 3 files each |
| Number |
1 u |
1 u - 450 |
450 |
| Value |
$4 |
$6 |
$6 |
| Total Value |
4 u |
6 u - $2700 |
$1800 |
Since 150 files were given free, there were 150 customers who bought two files each.
Number of files that each customer would get if they bought two files each and got 1 file free
= 2 + 1
= 3
Total number of files for customers who each bought two files
= 3 x 150
= 450
Number of files for customers who each bought 1 file = 1 u - 450
Total amount collected from customers who bought 1 file each
= 6 x (1 u - 450)
= 6 u - 2700
Total amount collected from customers who bought two files each
= 150 x 2 x 6
= $1800
Total amount collected from all the customers
= 6 u - 2700 + 1800
= 6 u - 900
Carl collected a total of $180 more than what he had paid for.
6 u - 900 = 4 u + 180
6 u - 4 u = 180 + 900
2 u = 1080
1 u = 1080 ÷ 2 = 540
Number of customers who bought just one file
= 1 u - 450
= 540 - 450
= 90
Answer(s): 90
