Riordan bought some pens at $2 each. He later sold them to his customers at $6 each. For customers who bought two pens were given another pen for free. The customers bought either one or two pens. Riordan gave away 200 free pens and collected a total of $1440 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 3 pens each |
| Number |
1 u |
1 u - 600 |
600 |
| Value |
$2 |
$6 |
$6 |
| Total Value |
2 u |
6 u - $3600 |
$2400 |
Since 200 pens were given free, there were 200 customers who bought two pens each.
Number of pens that each customer would get if they bought two pens each and got 1 pen free
= 2 + 1
= 3
Total number of pens for customers who each bought two pens
= 3 x 200
= 600
Number of pens for customers who each bought 1 pen = 1 u - 600
Total amount collected from customers who bought 1 pen each
= 6 x (1 u - 600)
= 6 u - 3600
Total amount collected from customers who bought two pens each
= 200 x 2 x 6
= $2400
Total amount collected from all the customers
= 6 u - 3600 + 2400
= 6 u - 1200
Riordan collected a total of $1440 more than what he had paid for.
6 u - 1200 = 2 u + 1440
6 u - 2 u = 1440 + 1200
4 u = 2640
1 u = 2640 ÷ 4 = 660
Number of customers who bought just one pen
= 1 u - 600
= 660 - 600
= 60
Answer(s): 60
