Cole bought some notebooks at $3 each. He later sold them to his customers at $5 each. For customers who bought two notebooks were given another notebook for free. The customers bought either one or two notebooks. Cole gave away 110 free notebooks and collected a total of $1010 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 - 330 |
330 |
Value |
$3 |
$5 |
$5 |
Total Value |
3 u |
5 u - $1650 |
$1100 |
Since 110 notebooks were given free, there were 110 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 110
= 330
Number of notebooks for customers who each bought 1 notebook = 1 u - 330
Total amount collected from customers who bought 1 notebook each
= 5 x (1 u - 330)
= 5 u - 1650
Total amount collected from customers who bought two notebooks each
= 110 x 2 x 5
= $1100
Total amount collected from all the customers
= 5 u - 1650 + 1100
= 5 u - 550
Cole collected a total of $1010 more than what he had paid for.
5 u - 550 = 3 u + 1010
5 u - 3 u = 1010 + 550
2 u = 1560
1 u = 1560 ÷ 2 = 780
Number of customers who bought just one notebook
= 1 u - 330
= 780 - 330
= 450
Answer(s): 450