Ivan bought some pens at $5 each. He later sold them to his customers at $10 each. For customers who bought four pens were given another pen for free. The customers bought either one or four pens. Ivan gave away 130 free pens and collected a total of $2150 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 5 pens each |
| Number |
1 u |
1 u - 650 |
650 |
| Value |
$5 |
$10 |
$10 |
| Total Value |
5 u |
10 u - $6500 |
$5200 |
Since 130 pens were given free, there were 130 customers who bought four pens each.
Number of pens that each customer would get if they bought four pens each and got 1 pen free
= 4 + 1
= 5
Total number of pens for customers who each bought four pens
= 5 x 130
= 650
Number of pens for customers who each bought 1 pen = 1 u - 650
Total amount collected from customers who bought 1 pen each
= 10 x (1 u - 650)
= 10 u - 6500
Total amount collected from customers who bought four pens each
= 130 x 4 x 10
= $5200
Total amount collected from all the customers
= 10 u - 6500 + 5200
= 10 u - 1300
Ivan collected a total of $2150 more than what he had paid for.
10 u - 1300 = 5 u + 2150
10 u - 5 u = 2150 + 1300
5 u = 3450
1 u = 3450 ÷ 5 = 690
Number of customers who bought just one pen
= 1 u - 650
= 690 - 650
= 40
Answer(s): 40
