Cole bought some notebooks at $3 each. He later sold them to his customers at $7 each. For customers who bought three notebooks were given another notebook for free. The customers bought either one or three notebooks. Cole gave away 120 free notebooks and collected a total of $2360 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 4 notebooks each |
| Number |
1 u |
1 u - 480 |
480 |
| Value |
$3 |
$7 |
$7 |
| Total Value |
3 u |
7 u - $3360 |
$2520 |
Since 120 notebooks were given free, there were 120 customers who bought three notebooks each.
Number of notebooks that each customer would get if they bought three notebooks each and got 1 notebook free
= 3 + 1
= 4
Total number of notebooks for customers who each bought three notebooks
= 4 x 120
= 480
Number of notebooks for customers who each bought 1 notebook = 1 u - 480
Total amount collected from customers who bought 1 notebook each
= 7 x (1 u - 480)
= 7 u - 3360
Total amount collected from customers who bought three notebooks each
= 120 x 3 x 7
= $2520
Total amount collected from all the customers
= 7 u - 3360 + 2520
= 7 u - 840
Cole collected a total of $2360 more than what he had paid for.
7 u - 840 = 3 u + 2360
7 u - 3 u = 2360 + 840
4 u = 3200
1 u = 3200 ÷ 4 = 800
Number of customers who bought just one notebook
= 1 u - 480
= 800 - 480
= 320
Answer(s): 320
