Ian bought some pens at $5 each. He later sold them to his customers at $7 each. For customers who bought two pens were given another pen for free. The customers bought either one or two pens. Ian gave away 170 free pens and collected a total of $370 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 - 510 |
510 |
| Value |
$5 |
$7 |
$7 |
| Total Value |
5 u |
7 u - $3570 |
$2380 |
Since 170 pens were given free, there were 170 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 170
= 510
Number of pens for customers who each bought 1 pen = 1 u - 510
Total amount collected from customers who bought 1 pen each
= 7 x (1 u - 510)
= 7 u - 3570
Total amount collected from customers who bought two pens each
= 170 x 2 x 7
= $2380
Total amount collected from all the customers
= 7 u - 3570 + 2380
= 7 u - 1190
Ian collected a total of $370 more than what he had paid for.
7 u - 1190 = 5 u + 370
7 u - 5 u = 370 + 1190
2 u = 1560
1 u = 1560 ÷ 2 = 780
Number of customers who bought just one pen
= 1 u - 510
= 780 - 510
= 270
Answer(s): 270
