Fabian bought some markers at $6 each. He later sold them to his customers at $11 each. For customers who bought two markers were given another marker for free. The customers bought either one or two markers. Fabian gave away 100 free markers and collected a total of $1400 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 - 300 |
300 |
Value |
$6 |
$11 |
$11 |
Total Value |
6 u |
11 u - $3300 |
$2200 |
Since 100 markers were given free, there were 100 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 100
= 300
Number of markers for customers who each bought 1 marker = 1 u - 300
Total amount collected from customers who bought 1 marker each
= 11 x (1 u - 300)
= 11 u - 3300
Total amount collected from customers who bought two markers each
= 100 x 2 x 11
= $2200
Total amount collected from all the customers
= 11 u - 3300 + 2200
= 11 u - 1100
Fabian collected a total of $1400 more than what he had paid for.
11 u - 1100 = 6 u + 1400
11 u - 6 u = 1400 + 1100
5 u = 2500
1 u = 2500 ÷ 5 = 500
Number of customers who bought just one marker
= 1 u - 300
= 500 - 300
= 200
Answer(s): 200