Zane bought some pencils at $6 each. He later sold them to his customers at $10 each. For customers who bought three pencils were given another pencil for free. The customers bought either one or three pencils. Zane gave away 160 free pencils and collected a total of $1440 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 4 pencils each |
| Number |
1 u |
1 u - 640 |
640 |
| Value |
$6 |
$10 |
$10 |
| Total Value |
6 u |
10 u - $6400 |
$4800 |
Since 160 pencils were given free, there were 160 customers who bought three pencils each.
Number of pencils that each customer would get if they bought three pencils each and got 1 pencil free
= 3 + 1
= 4
Total number of pencils for customers who each bought three pencils
= 4 x 160
= 640
Number of pencils for customers who each bought 1 pencil = 1 u - 640
Total amount collected from customers who bought 1 pencil each
= 10 x (1 u - 640)
= 10 u - 6400
Total amount collected from customers who bought three pencils each
= 160 x 3 x 10
= $4800
Total amount collected from all the customers
= 10 u - 6400 + 4800
= 10 u - 1600
Zane collected a total of $1440 more than what he had paid for.
10 u - 1600 = 6 u + 1440
10 u - 6 u = 1440 + 1600
4 u = 3040
1 u = 3040 ÷ 4 = 760
Number of customers who bought just one pencil
= 1 u - 640
= 760 - 640
= 120
Answer(s): 120
