Nick bought some pens at $3 each. He later sold them to his customers at $7 each. For customers who bought three pens were given another pen for free. The customers bought either one or three pens. Nick gave away 120 free pens and collected a total of $1920 more than what he had paid for. How many customers bought just one pen each?
|
Pens sold |
Pens given to customers who got 1 pen each |
Pens given to customers who got 4 pens each |
Number |
1 u |
1 u - 480 |
480 |
Value |
$3 |
$7 |
$7 |
Total Value |
3 u |
7 u - $3360 |
$2520 |
Since 120 pens were given free, there were 120 customers who bought three pens each.
Number of pens that each customer would get if they bought three pens each and got 1 pen free
= 3 + 1
= 4
Total number of pens for customers who each bought three pens
= 4 x 120
= 480
Number of pens for customers who each bought 1 pen = 1 u - 480
Total amount collected from customers who bought 1 pen each
= 7 x (1 u - 480)
= 7 u - 3360
Total amount collected from customers who bought three pens each
= 120 x 3 x 7
= $2520
Total amount collected from all the customers
= 7 u - 3360 + 2520
= 7 u - 840
Nick collected a total of $1920 more than what he had paid for.
7 u - 840 = 3 u + 1920
7 u - 3 u = 1920 + 840
4 u = 2760
1 u = 2760 ÷ 4 = 690
Number of customers who bought just one pen
= 1 u - 480
= 690 - 480
= 210
Answer(s): 210