Charlie bought some notebooks at $3 each. He later sold them to his customers at $8 each. For customers who bought two notebooks were given another notebook for free. The customers bought either one or two notebooks. Charlie gave away 220 free notebooks and collected a total of $1890 more than what he had paid for. How many customers bought just one notebook each?
|
Notebooks sold |
Notebooks given to customers who got 1 notebook each |
Notebooks given to customers who got 3 notebooks each |
Number |
1 u |
1 u - 660 |
660 |
Value |
$3 |
$8 |
$8 |
Total Value |
3 u |
8 u - $5280 |
$3520 |
Since 220 notebooks were given free, there were 220 customers who bought two notebooks each.
Number of notebooks that each customer would get if they bought two notebooks each and got 1 notebook free
= 2 + 1
= 3
Total number of notebooks for customers who each bought two notebooks
= 3 x 220
= 660
Number of notebooks for customers who each bought 1 notebook = 1 u - 660
Total amount collected from customers who bought 1 notebook each
= 8 x (1 u - 660)
= 8 u - 5280
Total amount collected from customers who bought two notebooks each
= 220 x 2 x 8
= $3520
Total amount collected from all the customers
= 8 u - 5280 + 3520
= 8 u - 1760
Charlie collected a total of $1890 more than what he had paid for.
8 u - 1760 = 3 u + 1890
8 u - 3 u = 1890 + 1760
5 u = 3650
1 u = 3650 ÷ 5 = 730
Number of customers who bought just one notebook
= 1 u - 660
= 730 - 660
= 70
Answer(s): 70