Luke bought some notebooks at $6 each. He later sold them to his customers at $9 each. For customers who bought two notebooks were given another notebook for free. The customers bought either one or two notebooks. Luke gave away 160 free notebooks and collected a total of $720 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 - 480 |
480 |
| Value |
$6 |
$9 |
$9 |
| Total Value |
6 u |
9 u - $4320 |
$2880 |
Since 160 notebooks were given free, there were 160 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 160
= 480
Number of notebooks for customers who each bought 1 notebook = 1 u - 480
Total amount collected from customers who bought 1 notebook each
= 9 x (1 u - 480)
= 9 u - 4320
Total amount collected from customers who bought two notebooks each
= 160 x 2 x 9
= $2880
Total amount collected from all the customers
= 9 u - 4320 + 2880
= 9 u - 1440
Luke collected a total of $720 more than what he had paid for.
9 u - 1440 = 6 u + 720
9 u - 6 u = 720 + 1440
3 u = 2160
1 u = 2160 ÷ 3 = 720
Number of customers who bought just one notebook
= 1 u - 480
= 720 - 480
= 240
Answer(s): 240
