Sam bought some pens at $6 each. He later sold them to his customers at $9 each. For customers who bought two pens were given another pen for free. The customers bought either one or two pens. Sam gave away 220 free pens and collected a total of $270 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 |
$6 |
$9 |
$9 |
| Total Value |
6 u |
9 u - $5940 |
$3960 |
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
= 9 x (1 u - 660)
= 9 u - 5940
Total amount collected from customers who bought two pens each
= 220 x 2 x 9
= $3960
Total amount collected from all the customers
= 9 u - 5940 + 3960
= 9 u - 1980
Sam collected a total of $270 more than what he had paid for.
9 u - 1980 = 6 u + 270
9 u - 6 u = 270 + 1980
3 u = 2250
1 u = 2250 ÷ 3 = 750
Number of customers who bought just one pen
= 1 u - 660
= 750 - 660
= 90
Answer(s): 90
