Wesley bought some pens at $4 each. He later sold them to his customers at $8 each. For customers who bought three pens were given another pen for free. The customers bought either one or three pens. Wesley gave away 130 free pens and collected a total of $1600 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 4 pens each |
| Number |
1 u |
1 u - 520 |
520 |
| Value |
$4 |
$8 |
$8 |
| Total Value |
4 u |
8 u - $4160 |
$3120 |
Since 130 pens were given free, there were 130 customers who bought three pens each.
Number of pens that each customer would get if they bought three pens each and got 1 pen free
= 3 + 1
= 4
Total number of pens for customers who each bought three pens
= 4 x 130
= 520
Number of pens for customers who each bought 1 pen = 1 u - 520
Total amount collected from customers who bought 1 pen each
= 8 x (1 u - 520)
= 8 u - 4160
Total amount collected from customers who bought three pens each
= 130 x 3 x 8
= $3120
Total amount collected from all the customers
= 8 u - 4160 + 3120
= 8 u - 1040
Wesley collected a total of $1600 more than what he had paid for.
8 u - 1040 = 4 u + 1600
8 u - 4 u = 1600 + 1040
4 u = 2640
1 u = 2640 ÷ 4 = 660
Number of customers who bought just one pen
= 1 u - 520
= 660 - 520
= 140
Answer(s): 140
