Liam bought some pens at $3 each. He later sold them to his customers at $5 each. For customers who bought two pens were given another pen for free. The customers bought either one or two pens. Liam gave away 160 free pens and collected a total of $660 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 - 480 |
480 |
| Value |
$3 |
$5 |
$5 |
| Total Value |
3 u |
5 u - $2400 |
$1600 |
Since 160 pens were given free, there were 160 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 160
= 480
Number of pens for customers who each bought 1 pen = 1 u - 480
Total amount collected from customers who bought 1 pen each
= 5 x (1 u - 480)
= 5 u - 2400
Total amount collected from customers who bought two pens each
= 160 x 2 x 5
= $1600
Total amount collected from all the customers
= 5 u - 2400 + 1600
= 5 u - 800
Liam collected a total of $660 more than what he had paid for.
5 u - 800 = 3 u + 660
5 u - 3 u = 660 + 800
2 u = 1460
1 u = 1460 ÷ 2 = 730
Number of customers who bought just one pen
= 1 u - 480
= 730 - 480
= 250
Answer(s): 250
