Elijah bought some markers at $2 each. He later sold them to his customers at $7 each. For customers who bought two markers were given another marker for free. The customers bought either one or two markers. Elijah gave away 160 free markers and collected a total of $2080 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 - 480 |
480 |
Value |
$2 |
$7 |
$7 |
Total Value |
2 u |
7 u - $3360 |
$2240 |
Since 160 markers were given free, there were 160 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 160
= 480
Number of markers for customers who each bought 1 marker = 1 u - 480
Total amount collected from customers who bought 1 marker each
= 7 x (1 u - 480)
= 7 u - 3360
Total amount collected from customers who bought two markers each
= 160 x 2 x 7
= $2240
Total amount collected from all the customers
= 7 u - 3360 + 2240
= 7 u - 1120
Elijah collected a total of $2080 more than what he had paid for.
7 u - 1120 = 2 u + 2080
7 u - 2 u = 2080 + 1120
5 u = 3200
1 u = 3200 ÷ 5 = 640
Number of customers who bought just one marker
= 1 u - 480
= 640 - 480
= 160
Answer(s): 160