Simon bought some markers at $3 each. He later sold them to his customers at $8 each. For customers who bought two markers were given another marker for free. The customers bought either one or two markers. Simon gave away 150 free markers and collected a total of $1800 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 - 450 |
450 |
Value |
$3 |
$8 |
$8 |
Total Value |
3 u |
8 u - $3600 |
$2400 |
Since 150 markers were given free, there were 150 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 150
= 450
Number of markers for customers who each bought 1 marker = 1 u - 450
Total amount collected from customers who bought 1 marker each
= 8 x (1 u - 450)
= 8 u - 3600
Total amount collected from customers who bought two markers each
= 150 x 2 x 8
= $2400
Total amount collected from all the customers
= 8 u - 3600 + 2400
= 8 u - 1200
Simon collected a total of $1800 more than what he had paid for.
8 u - 1200 = 3 u + 1800
8 u - 3 u = 1800 + 1200
5 u = 3000
1 u = 3000 ÷ 5 = 600
Number of customers who bought just one marker
= 1 u - 450
= 600 - 450
= 150
Answer(s): 150