Ken bought some pencils at $5 each. He later sold them to his customers at $8 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Ken gave away 160 free pencils and collected a total of $550 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 - 480 |
480 |
| Value |
$5 |
$8 |
$8 |
| Total Value |
5 u |
8 u - $3840 |
$2560 |
Since 160 pencils were given free, there were 160 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 160
= 480
Number of pencils for customers who each bought 1 pencil = 1 u - 480
Total amount collected from customers who bought 1 pencil each
= 8 x (1 u - 480)
= 8 u - 3840
Total amount collected from customers who bought two pencils each
= 160 x 2 x 8
= $2560
Total amount collected from all the customers
= 8 u - 3840 + 2560
= 8 u - 1280
Ken collected a total of $550 more than what he had paid for.
8 u - 1280 = 5 u + 550
8 u - 5 u = 550 + 1280
3 u = 1830
1 u = 1830 ÷ 3 = 610
Number of customers who bought just one pencil
= 1 u - 480
= 610 - 480
= 130
Answer(s): 130
