Bobby bought some pens at $6 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. Bobby gave away 180 free pens and collected a total of $120 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 - 540 |
540 |
| Value |
$6 |
$8 |
$8 |
| Total Value |
6 u |
8 u - $4320 |
$2880 |
Since 180 pens were given free, there were 180 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 180
= 540
Number of pens for customers who each bought 1 pen = 1 u - 540
Total amount collected from customers who bought 1 pen each
= 8 x (1 u - 540)
= 8 u - 4320
Total amount collected from customers who bought two pens each
= 180 x 2 x 8
= $2880
Total amount collected from all the customers
= 8 u - 4320 + 2880
= 8 u - 1440
Bobby collected a total of $120 more than what he had paid for.
8 u - 1440 = 6 u + 120
8 u - 6 u = 120 + 1440
2 u = 1560
1 u = 1560 ÷ 2 = 780
Number of customers who bought just one pen
= 1 u - 540
= 780 - 540
= 240
Answer(s): 240
