Ben bought some notebooks at $6 each. He later sold them to his customers at $11 each. For customers who bought two notebooks were given another notebook for free. The customers bought either one or two notebooks. Ben gave away 130 free notebooks and collected a total of $2420 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 - 390 |
390 |
| Value |
$6 |
$11 |
$11 |
| Total Value |
6 u |
11 u - $4290 |
$2860 |
Since 130 notebooks were given free, there were 130 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 130
= 390
Number of notebooks for customers who each bought 1 notebook = 1 u - 390
Total amount collected from customers who bought 1 notebook each
= 11 x (1 u - 390)
= 11 u - 4290
Total amount collected from customers who bought two notebooks each
= 130 x 2 x 11
= $2860
Total amount collected from all the customers
= 11 u - 4290 + 2860
= 11 u - 1430
Ben collected a total of $2420 more than what he had paid for.
11 u - 1430 = 6 u + 2420
11 u - 6 u = 2420 + 1430
5 u = 3850
1 u = 3850 ÷ 5 = 770
Number of customers who bought just one notebook
= 1 u - 390
= 770 - 390
= 380
Answer(s): 380
