Nick bought some pens at $6 each. He later sold them to his customers at $11 each. For customers who bought two pens were given another pen for free. The customers bought either one or two pens. Nick gave away 110 free pens and collected a total of $2740 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 - 330 |
330 |
| Value |
$6 |
$11 |
$11 |
| Total Value |
6 u |
11 u - $3630 |
$2420 |
Since 110 pens were given free, there were 110 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 110
= 330
Number of pens for customers who each bought 1 pen = 1 u - 330
Total amount collected from customers who bought 1 pen each
= 11 x (1 u - 330)
= 11 u - 3630
Total amount collected from customers who bought two pens each
= 110 x 2 x 11
= $2420
Total amount collected from all the customers
= 11 u - 3630 + 2420
= 11 u - 1210
Nick collected a total of $2740 more than what he had paid for.
11 u - 1210 = 6 u + 2740
11 u - 6 u = 2740 + 1210
5 u = 3950
1 u = 3950 ÷ 5 = 790
Number of customers who bought just one pen
= 1 u - 330
= 790 - 330
= 460
Answer(s): 460
