Albert bought some notebooks at $6 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. Albert gave away 230 free notebooks and collected a total of $820 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 - 690 |
690 |
| Value |
$6 |
$10 |
$10 |
| Total Value |
6 u |
10 u - $6900 |
$4600 |
Since 230 notebooks were given free, there were 230 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 230
= 690
Number of notebooks for customers who each bought 1 notebook = 1 u - 690
Total amount collected from customers who bought 1 notebook each
= 10 x (1 u - 690)
= 10 u - 6900
Total amount collected from customers who bought two notebooks each
= 230 x 2 x 10
= $4600
Total amount collected from all the customers
= 10 u - 6900 + 4600
= 10 u - 2300
Albert collected a total of $820 more than what he had paid for.
10 u - 2300 = 6 u + 820
10 u - 6 u = 820 + 2300
4 u = 3120
1 u = 3120 ÷ 4 = 780
Number of customers who bought just one notebook
= 1 u - 690
= 780 - 690
= 90
Answer(s): 90
