Paul bought some pens at $5 each. He later sold them to his customers at $8 each. For customers who bought three pens were given another pen for free. The customers bought either one or three pens. Paul gave away 180 free pens and collected a total of $750 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 - 720 |
720 |
| Value |
$5 |
$8 |
$8 |
| Total Value |
5 u |
8 u - $5760 |
$4320 |
Since 180 pens were given free, there were 180 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 180
= 720
Number of pens for customers who each bought 1 pen = 1 u - 720
Total amount collected from customers who bought 1 pen each
= 8 x (1 u - 720)
= 8 u - 5760
Total amount collected from customers who bought three pens each
= 180 x 3 x 8
= $4320
Total amount collected from all the customers
= 8 u - 5760 + 4320
= 8 u - 1440
Paul collected a total of $750 more than what he had paid for.
8 u - 1440 = 5 u + 750
8 u - 5 u = 750 + 1440
3 u = 2190
1 u = 2190 ÷ 3 = 730
Number of customers who bought just one pen
= 1 u - 720
= 730 - 720
= 10
Answer(s): 10
