Owen bought some markers at $5 each. He later sold them to his customers at $10 each. For customers who bought two markers were given another marker for free. The customers bought either one or two markers. Owen gave away 130 free markers and collected a total of $2000 more than what he had paid for. How many customers bought just one marker each?
|
Markers sold |
Markers given to customers who got 1 marker each |
Markers given to customers who got 3 markers each |
Number |
1 u |
1 u - 390 |
390 |
Value |
$5 |
$10 |
$10 |
Total Value |
5 u |
10 u - $3900 |
$2600 |
Since 130 markers were given free, there were 130 customers who bought two markers each.
Number of markers that each customer would get if they bought two markers each and got 1 marker free
= 2 + 1
= 3
Total number of markers for customers who each bought two markers
= 3 x 130
= 390
Number of markers for customers who each bought 1 marker = 1 u - 390
Total amount collected from customers who bought 1 marker each
= 10 x (1 u - 390)
= 10 u - 3900
Total amount collected from customers who bought two markers each
= 130 x 2 x 10
= $2600
Total amount collected from all the customers
= 10 u - 3900 + 2600
= 10 u - 1300
Owen collected a total of $2000 more than what he had paid for.
10 u - 1300 = 5 u + 2000
10 u - 5 u = 2000 + 1300
5 u = 3300
1 u = 3300 ÷ 5 = 660
Number of customers who bought just one marker
= 1 u - 390
= 660 - 390
= 270
Answer(s): 270