Ben bought some markers at $2 each. He later sold them to his customers at $6 each. For customers who bought three markers were given another marker for free. The customers bought either one or three markers. Ben gave away 130 free markers and collected a total of $2300 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 4 markers each |
Number |
1 u |
1 u - 520 |
520 |
Value |
$2 |
$6 |
$6 |
Total Value |
2 u |
6 u - $3120 |
$2340 |
Since 130 markers were given free, there were 130 customers who bought three markers each.
Number of markers that each customer would get if they bought three markers each and got 1 marker free
= 3 + 1
= 4
Total number of markers for customers who each bought three markers
= 4 x 130
= 520
Number of markers for customers who each bought 1 marker = 1 u - 520
Total amount collected from customers who bought 1 marker each
= 6 x (1 u - 520)
= 6 u - 3120
Total amount collected from customers who bought three markers each
= 130 x 3 x 6
= $2340
Total amount collected from all the customers
= 6 u - 3120 + 2340
= 6 u - 780
Ben collected a total of $2300 more than what he had paid for.
6 u - 780 = 2 u + 2300
6 u - 2 u = 2300 + 780
4 u = 3080
1 u = 3080 ÷ 4 = 770
Number of customers who bought just one marker
= 1 u - 520
= 770 - 520
= 250
Answer(s): 250