Sean bought some notebooks at $5 each. He later sold them to his customers at $9 each. For customers who bought three notebooks were given another notebook for free. The customers bought either one or three notebooks. Sean gave away 130 free notebooks and collected a total of $1310 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 - 520 |
520 |
| Value |
$5 |
$9 |
$9 |
| Total Value |
5 u |
9 u - $4680 |
$3510 |
Since 130 notebooks were given free, there were 130 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 130
= 520
Number of notebooks for customers who each bought 1 notebook = 1 u - 520
Total amount collected from customers who bought 1 notebook each
= 9 x (1 u - 520)
= 9 u - 4680
Total amount collected from customers who bought three notebooks each
= 130 x 3 x 9
= $3510
Total amount collected from all the customers
= 9 u - 4680 + 3510
= 9 u - 1170
Sean collected a total of $1310 more than what he had paid for.
9 u - 1170 = 5 u + 1310
9 u - 5 u = 1310 + 1170
4 u = 2480
1 u = 2480 ÷ 4 = 620
Number of customers who bought just one notebook
= 1 u - 520
= 620 - 520
= 100
Answer(s): 100
