Ivan 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. Ivan gave away 150 free notebooks and collected a total of $850 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 - 450 |
450 |
Value |
$3 |
$5 |
$5 |
Total Value |
3 u |
5 u - $2250 |
$1500 |
Since 150 notebooks were given free, there were 150 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 150
= 450
Number of notebooks for customers who each bought 1 notebook = 1 u - 450
Total amount collected from customers who bought 1 notebook each
= 5 x (1 u - 450)
= 5 u - 2250
Total amount collected from customers who bought two notebooks each
= 150 x 2 x 5
= $1500
Total amount collected from all the customers
= 5 u - 2250 + 1500
= 5 u - 750
Ivan collected a total of $850 more than what he had paid for.
5 u - 750 = 3 u + 850
5 u - 3 u = 850 + 750
2 u = 1600
1 u = 1600 ÷ 2 = 800
Number of customers who bought just one notebook
= 1 u - 450
= 800 - 450
= 350
Answer(s): 350