Peter bought some notebooks at $4 each. He later sold them to his customers at $7 each. For customers who bought two notebooks were given another notebook for free. The customers bought either one or two notebooks. Peter gave away 250 free notebooks and collected a total of $590 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 - 750 |
750 |
Value |
$4 |
$7 |
$7 |
Total Value |
4 u |
7 u - $5250 |
$3500 |
Since 250 notebooks were given free, there were 250 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 250
= 750
Number of notebooks for customers who each bought 1 notebook = 1 u - 750
Total amount collected from customers who bought 1 notebook each
= 7 x (1 u - 750)
= 7 u - 5250
Total amount collected from customers who bought two notebooks each
= 250 x 2 x 7
= $3500
Total amount collected from all the customers
= 7 u - 5250 + 3500
= 7 u - 1750
Peter collected a total of $590 more than what he had paid for.
7 u - 1750 = 4 u + 590
7 u - 4 u = 590 + 1750
3 u = 2340
1 u = 2340 ÷ 3 = 780
Number of customers who bought just one notebook
= 1 u - 750
= 780 - 750
= 30
Answer(s): 30