Riordan bought some notebooks at $4 each. He later sold them to his customers at $8 each. For customers who bought two notebooks were given another notebook for free. The customers bought either one or two notebooks. Riordan gave away 100 free notebooks and collected a total of $800 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 - 300 |
300 |
| Value |
$4 |
$8 |
$8 |
| Total Value |
4 u |
8 u - $2400 |
$1600 |
Since 100 notebooks were given free, there were 100 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 100
= 300
Number of notebooks for customers who each bought 1 notebook = 1 u - 300
Total amount collected from customers who bought 1 notebook each
= 8 x (1 u - 300)
= 8 u - 2400
Total amount collected from customers who bought two notebooks each
= 100 x 2 x 8
= $1600
Total amount collected from all the customers
= 8 u - 2400 + 1600
= 8 u - 800
Riordan collected a total of $800 more than what he had paid for.
8 u - 800 = 4 u + 800
8 u - 4 u = 800 + 800
4 u = 1600
1 u = 1600 ÷ 4 = 400
Number of customers who bought just one notebook
= 1 u - 300
= 400 - 300
= 100
Answer(s): 100
