Pierre bought some files at $3 each. He later sold them to his customers at $6 each. For customers who bought four files were given another file for free. The customers bought either one or four files. Pierre gave away 140 free files and collected a total of $1350 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 5 files each |
| Number |
1 u |
1 u - 700 |
700 |
| Value |
$3 |
$6 |
$6 |
| Total Value |
3 u |
6 u - $4200 |
$3360 |
Since 140 files were given free, there were 140 customers who bought four files each.
Number of files that each customer would get if they bought four files each and got 1 file free
= 4 + 1
= 5
Total number of files for customers who each bought four files
= 5 x 140
= 700
Number of files for customers who each bought 1 file = 1 u - 700
Total amount collected from customers who bought 1 file each
= 6 x (1 u - 700)
= 6 u - 4200
Total amount collected from customers who bought four files each
= 140 x 4 x 6
= $3360
Total amount collected from all the customers
= 6 u - 4200 + 3360
= 6 u - 840
Pierre collected a total of $1350 more than what he had paid for.
6 u - 840 = 3 u + 1350
6 u - 3 u = 1350 + 840
3 u = 2190
1 u = 2190 ÷ 3 = 730
Number of customers who bought just one file
= 1 u - 700
= 730 - 700
= 30
Answer(s): 30
