Ryan bought some markers at $6 each. He later sold them to his customers at $10 each. For customers who bought two markers were given another marker for free. The customers bought either one or two markers. Ryan gave away 100 free markers and collected a total of $1360 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 |
$10 |
$10 |
| Total Value |
6 u |
10 u - $3000 |
$2000 |
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
= 10 x (1 u - 300)
= 10 u - 3000
Total amount collected from customers who bought two markers each
= 100 x 2 x 10
= $2000
Total amount collected from all the customers
= 10 u - 3000 + 2000
= 10 u - 1000
Ryan collected a total of $1360 more than what he had paid for.
10 u - 1000 = 6 u + 1360
10 u - 6 u = 1360 + 1000
4 u = 2360
1 u = 2360 ÷ 4 = 590
Number of customers who bought just one marker
= 1 u - 300
= 590 - 300
= 290
Answer(s): 290
