Fred bought some markers at $3 each. He later sold them to his customers at $8 each. For customers who bought three markers were given another marker for free. The customers bought either one or three markers. Fred gave away 150 free markers and collected a total of $2400 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 - 600 |
600 |
Value |
$3 |
$8 |
$8 |
Total Value |
3 u |
8 u - $4800 |
$3600 |
Since 150 markers were given free, there were 150 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 150
= 600
Number of markers for customers who each bought 1 marker = 1 u - 600
Total amount collected from customers who bought 1 marker each
= 8 x (1 u - 600)
= 8 u - 4800
Total amount collected from customers who bought three markers each
= 150 x 3 x 8
= $3600
Total amount collected from all the customers
= 8 u - 4800 + 3600
= 8 u - 1200
Fred collected a total of $2400 more than what he had paid for.
8 u - 1200 = 3 u + 2400
8 u - 3 u = 2400 + 1200
5 u = 3600
1 u = 3600 ÷ 5 = 720
Number of customers who bought just one marker
= 1 u - 600
= 720 - 600
= 120
Answer(s): 120