Gabriel bought some files at $3 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. Gabriel gave away 190 free files and collected a total of $690 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 - 570 |
570 |
| Value |
$3 |
$6 |
$6 |
| Total Value |
3 u |
6 u - $3420 |
$2280 |
Since 190 files were given free, there were 190 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 190
= 570
Number of files for customers who each bought 1 file = 1 u - 570
Total amount collected from customers who bought 1 file each
= 6 x (1 u - 570)
= 6 u - 3420
Total amount collected from customers who bought two files each
= 190 x 2 x 6
= $2280
Total amount collected from all the customers
= 6 u - 3420 + 2280
= 6 u - 1140
Gabriel collected a total of $690 more than what he had paid for.
6 u - 1140 = 3 u + 690
6 u - 3 u = 690 + 1140
3 u = 1830
1 u = 1830 ÷ 3 = 610
Number of customers who bought just one file
= 1 u - 570
= 610 - 570
= 40
Answer(s): 40
