Sean bought some pencils at $5 each. He later sold them to his customers at $9 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Sean gave away 200 free pencils and collected a total of $1200 more than what he had paid for. How many customers bought just one pencil each?
|
Pencils sold |
Pencils given to customers who got 1 pencil each |
Pencils given to customers who got 3 pencils each |
Number |
1 u |
1 u - 600 |
600 |
Value |
$5 |
$9 |
$9 |
Total Value |
5 u |
9 u - $5400 |
$3600 |
Since 200 pencils were given free, there were 200 customers who bought two pencils each.
Number of pencils that each customer would get if they bought two pencils each and got 1 pencil free
= 2 + 1
= 3
Total number of pencils for customers who each bought two pencils
= 3 x 200
= 600
Number of pencils for customers who each bought 1 pencil = 1 u - 600
Total amount collected from customers who bought 1 pencil each
= 9 x (1 u - 600)
= 9 u - 5400
Total amount collected from customers who bought two pencils each
= 200 x 2 x 9
= $3600
Total amount collected from all the customers
= 9 u - 5400 + 3600
= 9 u - 1800
Sean collected a total of $1200 more than what he had paid for.
9 u - 1800 = 5 u + 1200
9 u - 5 u = 1200 + 1800
4 u = 3000
1 u = 3000 ÷ 4 = 750
Number of customers who bought just one pencil
= 1 u - 600
= 750 - 600
= 150
Answer(s): 150