Neave bought some pencils at $2 each. He later sold them to his customers at $4 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Neave gave away 180 free pencils and collected a total of $460 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 - 540	540
Value	$2	$4	$4
Total Value	2 u	4 u - $2160	$1440

Since 180 pencils were given free, there were 180 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 180
= 540

Number of pencils for customers who each bought 1 pencil = 1 u - 540

Total amount collected from customers who bought 1 pencil each
= 4 x (1 u - 540)
= 4 u - 2160

Total amount collected from customers who bought two pencils each
= 180 x 2 x 4
= $1440

Total amount collected from all the customers
= 4 u - 2160 + 1440
= 4 u - 720

Neave collected a total of $460 more than what he had paid for.

4 u - 720 = 2 u + 460
4 u - 2 u = 460 + 720
2 u = 1180

1 u = 1180 ÷ 2 = 590

Number of customers who bought just one pencil
= 1 u - 540
= 590 - 540
= 50

Answer(s): 50