Eric bought some pens at $3 each. He later sold them to his customers at $8 each. For customers who bought two pens were given another pen for free. The customers bought either one or two pens. Eric gave away 220 free pens and collected a total of $1890 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 - 660 |
660 |
| Value |
$3 |
$8 |
$8 |
| Total Value |
3 u |
8 u - $5280 |
$3520 |
Since 220 pens were given free, there were 220 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 220
= 660
Number of pens for customers who each bought 1 pen = 1 u - 660
Total amount collected from customers who bought 1 pen each
= 8 x (1 u - 660)
= 8 u - 5280
Total amount collected from customers who bought two pens each
= 220 x 2 x 8
= $3520
Total amount collected from all the customers
= 8 u - 5280 + 3520
= 8 u - 1760
Eric collected a total of $1890 more than what he had paid for.
8 u - 1760 = 3 u + 1890
8 u - 3 u = 1890 + 1760
5 u = 3650
1 u = 3650 ÷ 5 = 730
Number of customers who bought just one pen
= 1 u - 660
= 730 - 660
= 70
Answer(s): 70
