Luke bought some pens at $4 each. He later sold them to his customers at $9 each. For customers who bought four pens were given another pen for free. The customers bought either one or four pens. Luke gave away 120 free pens and collected a total of $2670 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 5 pens each |
| Number |
1 u |
1 u - 600 |
600 |
| Value |
$4 |
$9 |
$9 |
| Total Value |
4 u |
9 u - $5400 |
$4320 |
Since 120 pens were given free, there were 120 customers who bought four pens each.
Number of pens that each customer would get if they bought four pens each and got 1 pen free
= 4 + 1
= 5
Total number of pens for customers who each bought four pens
= 5 x 120
= 600
Number of pens for customers who each bought 1 pen = 1 u - 600
Total amount collected from customers who bought 1 pen each
= 9 x (1 u - 600)
= 9 u - 5400
Total amount collected from customers who bought four pens each
= 120 x 4 x 9
= $4320
Total amount collected from all the customers
= 9 u - 5400 + 4320
= 9 u - 1080
Luke collected a total of $2670 more than what he had paid for.
9 u - 1080 = 4 u + 2670
9 u - 4 u = 2670 + 1080
5 u = 3750
1 u = 3750 ÷ 5 = 750
Number of customers who bought just one pen
= 1 u - 600
= 750 - 600
= 150
Answer(s): 150
