Zane bought some markers at $4 each. He later sold them to his customers at $9 each. For customers who bought two markers were given another marker for free. The customers bought either one or two markers. Zane gave away 110 free markers and collected a total of $1710 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 - 330 |
330 |
Value |
$4 |
$9 |
$9 |
Total Value |
4 u |
9 u - $2970 |
$1980 |
Since 110 markers were given free, there were 110 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 110
= 330
Number of markers for customers who each bought 1 marker = 1 u - 330
Total amount collected from customers who bought 1 marker each
= 9 x (1 u - 330)
= 9 u - 2970
Total amount collected from customers who bought two markers each
= 110 x 2 x 9
= $1980
Total amount collected from all the customers
= 9 u - 2970 + 1980
= 9 u - 990
Zane collected a total of $1710 more than what he had paid for.
9 u - 990 = 4 u + 1710
9 u - 4 u = 1710 + 990
5 u = 2700
1 u = 2700 ÷ 5 = 540
Number of customers who bought just one marker
= 1 u - 330
= 540 - 330
= 210
Answer(s): 210