Justin bought some notebooks at $3 each. He later sold them to his customers at $6 each. For customers who bought four notebooks were given another notebook for free. The customers bought either one or four notebooks. Justin gave away 110 free notebooks and collected a total of $1020 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 - 550 |
550 |
Value |
$3 |
$6 |
$6 |
Total Value |
3 u |
6 u - $3300 |
$2640 |
Since 110 notebooks were given free, there were 110 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 110
= 550
Number of notebooks for customers who each bought 1 notebook = 1 u - 550
Total amount collected from customers who bought 1 notebook each
= 6 x (1 u - 550)
= 6 u - 3300
Total amount collected from customers who bought four notebooks each
= 110 x 4 x 6
= $2640
Total amount collected from all the customers
= 6 u - 3300 + 2640
= 6 u - 660
Justin collected a total of $1020 more than what he had paid for.
6 u - 660 = 3 u + 1020
6 u - 3 u = 1020 + 660
3 u = 1680
1 u = 1680 ÷ 3 = 560
Number of customers who bought just one notebook
= 1 u - 550
= 560 - 550
= 10
Answer(s): 10