Rael bought some files at $2 each. He later sold them to his customers at $7 each. For customers who bought two files were given another file for free. The customers bought either one or two files. Rael gave away 120 free files and collected a total of $2110 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 - 360 |
360 |
Value |
$2 |
$7 |
$7 |
Total Value |
2 u |
7 u - $2520 |
$1680 |
Since 120 files were given free, there were 120 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 120
= 360
Number of files for customers who each bought 1 file = 1 u - 360
Total amount collected from customers who bought 1 file each
= 7 x (1 u - 360)
= 7 u - 2520
Total amount collected from customers who bought two files each
= 120 x 2 x 7
= $1680
Total amount collected from all the customers
= 7 u - 2520 + 1680
= 7 u - 840
Rael collected a total of $2110 more than what he had paid for.
7 u - 840 = 2 u + 2110
7 u - 2 u = 2110 + 840
5 u = 2950
1 u = 2950 ÷ 5 = 590
Number of customers who bought just one file
= 1 u - 360
= 590 - 360
= 230
Answer(s): 230