Vincent bought some markers at $5 each. He later sold them to his customers at $10 each. For customers who bought three markers were given another marker for free. The customers bought either one or three markers. Vincent gave away 100 free markers and collected a total of $2650 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 - 400 |
400 |
| Value |
$5 |
$10 |
$10 |
| Total Value |
5 u |
10 u - $4000 |
$3000 |
Since 100 markers were given free, there were 100 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 100
= 400
Number of markers for customers who each bought 1 marker = 1 u - 400
Total amount collected from customers who bought 1 marker each
= 10 x (1 u - 400)
= 10 u - 4000
Total amount collected from customers who bought three markers each
= 100 x 3 x 10
= $3000
Total amount collected from all the customers
= 10 u - 4000 + 3000
= 10 u - 1000
Vincent collected a total of $2650 more than what he had paid for.
10 u - 1000 = 5 u + 2650
10 u - 5 u = 2650 + 1000
5 u = 3650
1 u = 3650 ÷ 5 = 730
Number of customers who bought just one marker
= 1 u - 400
= 730 - 400
= 330
Answer(s): 330
