Oliver bought some notebooks at $5 each. He later sold them to his customers at $10 each. For customers who bought three notebooks were given another notebook for free. The customers bought either one or three notebooks. Oliver gave away 100 free notebooks and collected a total of $1200 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 - 400 |
400 |
Value |
$5 |
$10 |
$10 |
Total Value |
5 u |
10 u - $4000 |
$3000 |
Since 100 notebooks were given free, there were 100 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 100
= 400
Number of notebooks for customers who each bought 1 notebook = 1 u - 400
Total amount collected from customers who bought 1 notebook each
= 10 x (1 u - 400)
= 10 u - 4000
Total amount collected from customers who bought three notebooks each
= 100 x 3 x 10
= $3000
Total amount collected from all the customers
= 10 u - 4000 + 3000
= 10 u - 1000
Oliver collected a total of $1200 more than what he had paid for.
10 u - 1000 = 5 u + 1200
10 u - 5 u = 1200 + 1000
5 u = 2200
1 u = 2200 ÷ 5 = 440
Number of customers who bought just one notebook
= 1 u - 400
= 440 - 400
= 40
Answer(s): 40