Fred bought some pens at $6 each. He later sold them to his customers at $8 each. For customers who bought four pens were given another pen for free. The customers bought either one or four pens. Fred gave away 150 free pens and collected a total of $320 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 - 750 |
750 |
Value |
$6 |
$8 |
$8 |
Total Value |
6 u |
8 u - $6000 |
$4800 |
Since 150 pens were given free, there were 150 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 150
= 750
Number of pens for customers who each bought 1 pen = 1 u - 750
Total amount collected from customers who bought 1 pen each
= 8 x (1 u - 750)
= 8 u - 6000
Total amount collected from customers who bought four pens each
= 150 x 4 x 8
= $4800
Total amount collected from all the customers
= 8 u - 6000 + 4800
= 8 u - 1200
Fred collected a total of $320 more than what he had paid for.
8 u - 1200 = 6 u + 320
8 u - 6 u = 320 + 1200
2 u = 1520
1 u = 1520 ÷ 2 = 760
Number of customers who bought just one pen
= 1 u - 750
= 760 - 750
= 10
Answer(s): 10