Bryan bought some notebooks at $3 each. He later sold them to his customers at $8 each. For customers who bought three notebooks were given another notebook for free. The customers bought either one or three notebooks. Bryan gave away 110 free notebooks and collected a total of $1820 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 - 440 |
440 |
Value |
$3 |
$8 |
$8 |
Total Value |
3 u |
8 u - $3520 |
$2640 |
Since 110 notebooks were given free, there were 110 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 110
= 440
Number of notebooks for customers who each bought 1 notebook = 1 u - 440
Total amount collected from customers who bought 1 notebook each
= 8 x (1 u - 440)
= 8 u - 3520
Total amount collected from customers who bought three notebooks each
= 110 x 3 x 8
= $2640
Total amount collected from all the customers
= 8 u - 3520 + 2640
= 8 u - 880
Bryan collected a total of $1820 more than what he had paid for.
8 u - 880 = 3 u + 1820
8 u - 3 u = 1820 + 880
5 u = 2700
1 u = 2700 ÷ 5 = 540
Number of customers who bought just one notebook
= 1 u - 440
= 540 - 440
= 100
Answer(s): 100