Jack 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. Jack gave away 120 free notebooks and collected a total of $700 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 - 360 |
360 |
Value |
$3 |
$5 |
$5 |
Total Value |
3 u |
5 u - $1800 |
$1200 |
Since 120 notebooks were given free, there were 120 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 120
= 360
Number of notebooks for customers who each bought 1 notebook = 1 u - 360
Total amount collected from customers who bought 1 notebook each
= 5 x (1 u - 360)
= 5 u - 1800
Total amount collected from customers who bought two notebooks each
= 120 x 2 x 5
= $1200
Total amount collected from all the customers
= 5 u - 1800 + 1200
= 5 u - 600
Jack collected a total of $700 more than what he had paid for.
5 u - 600 = 3 u + 700
5 u - 3 u = 700 + 600
2 u = 1300
1 u = 1300 ÷ 2 = 650
Number of customers who bought just one notebook
= 1 u - 360
= 650 - 360
= 290
Answer(s): 290