Tommy bought some notebooks at $6 each. He later sold them to his customers at $11 each. For customers who bought two notebooks were given another notebook for free. The customers bought either one or two notebooks. Tommy gave away 140 free notebooks and collected a total of $1660 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 - 420 |
420 |
| Value |
$6 |
$11 |
$11 |
| Total Value |
6 u |
11 u - $4620 |
$3080 |
Since 140 notebooks were given free, there were 140 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 140
= 420
Number of notebooks for customers who each bought 1 notebook = 1 u - 420
Total amount collected from customers who bought 1 notebook each
= 11 x (1 u - 420)
= 11 u - 4620
Total amount collected from customers who bought two notebooks each
= 140 x 2 x 11
= $3080
Total amount collected from all the customers
= 11 u - 4620 + 3080
= 11 u - 1540
Tommy collected a total of $1660 more than what he had paid for.
11 u - 1540 = 6 u + 1660
11 u - 6 u = 1660 + 1540
5 u = 3200
1 u = 3200 ÷ 5 = 640
Number of customers who bought just one notebook
= 1 u - 420
= 640 - 420
= 220
Answer(s): 220
