Warren bought some notebooks at $5 each. He later sold them to his customers at $10 each. For customers who bought two notebooks were given another notebook for free. The customers bought either one or two notebooks. Warren gave away 110 free notebooks and collected a total of $1800 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 - 330 |
330 |
| Value |
$5 |
$10 |
$10 |
| Total Value |
5 u |
10 u - $3300 |
$2200 |
Since 110 notebooks were given free, there were 110 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 110
= 330
Number of notebooks for customers who each bought 1 notebook = 1 u - 330
Total amount collected from customers who bought 1 notebook each
= 10 x (1 u - 330)
= 10 u - 3300
Total amount collected from customers who bought two notebooks each
= 110 x 2 x 10
= $2200
Total amount collected from all the customers
= 10 u - 3300 + 2200
= 10 u - 1100
Warren collected a total of $1800 more than what he had paid for.
10 u - 1100 = 5 u + 1800
10 u - 5 u = 1800 + 1100
5 u = 2900
1 u = 2900 ÷ 5 = 580
Number of customers who bought just one notebook
= 1 u - 330
= 580 - 330
= 250
Answer(s): 250
