Bryan bought some notebooks at $6 each. He later sold them to his customers at $10 each. For customers who bought four notebooks were given another notebook for free. The customers bought either one or four notebooks. Bryan gave away 100 free notebooks and collected a total of $1400 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 5 notebooks each |
Number |
1 u |
1 u - 500 |
500 |
Value |
$6 |
$10 |
$10 |
Total Value |
6 u |
10 u - $5000 |
$4000 |
Since 100 notebooks were given free, there were 100 customers who bought four notebooks each.
Number of notebooks that each customer would get if they bought four notebooks each and got 1 notebook free
= 4 + 1
= 5
Total number of notebooks for customers who each bought four notebooks
= 5 x 100
= 500
Number of notebooks for customers who each bought 1 notebook = 1 u - 500
Total amount collected from customers who bought 1 notebook each
= 10 x (1 u - 500)
= 10 u - 5000
Total amount collected from customers who bought four notebooks each
= 100 x 4 x 10
= $4000
Total amount collected from all the customers
= 10 u - 5000 + 4000
= 10 u - 1000
Bryan collected a total of $1400 more than what he had paid for.
10 u - 1000 = 6 u + 1400
10 u - 6 u = 1400 + 1000
4 u = 2400
1 u = 2400 ÷ 4 = 600
Number of customers who bought just one notebook
= 1 u - 500
= 600 - 500
= 100
Answer(s): 100