Vaidev bought some markers at $4 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. Vaidev gave away 230 free markers and collected a total of $1000 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 - 690 |
690 |
Value |
$4 |
$8 |
$8 |
Total Value |
4 u |
8 u - $5520 |
$3680 |
Since 230 markers were given free, there were 230 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 230
= 690
Number of markers for customers who each bought 1 marker = 1 u - 690
Total amount collected from customers who bought 1 marker each
= 8 x (1 u - 690)
= 8 u - 5520
Total amount collected from customers who bought two markers each
= 230 x 2 x 8
= $3680
Total amount collected from all the customers
= 8 u - 5520 + 3680
= 8 u - 1840
Vaidev collected a total of $1000 more than what he had paid for.
8 u - 1840 = 4 u + 1000
8 u - 4 u = 1000 + 1840
4 u = 2840
1 u = 2840 ÷ 4 = 710
Number of customers who bought just one marker
= 1 u - 690
= 710 - 690
= 20
Answer(s): 20