Perry bought some pencils at $4 each. He later sold them to his customers at $6 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Perry gave away 170 free pencils and collected a total of $420 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 - 510	510
Value	$4	$6	$6
Total Value	4 u	6 u - $3060	$2040

Since 170 pencils were given free, there were 170 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 170
= 510

Number of pencils for customers who each bought 1 pencil = 1 u - 510

Total amount collected from customers who bought 1 pencil each
= 6 x (1 u - 510)
= 6 u - 3060

Total amount collected from customers who bought two pencils each
= 170 x 2 x 6
= $2040

Total amount collected from all the customers
= 6 u - 3060 + 2040
= 6 u - 1020

Perry collected a total of $420 more than what he had paid for.

6 u - 1020 = 4 u + 420
6 u - 4 u = 420 + 1020
2 u = 1440

1 u = 1440 ÷ 2 = 720

Number of customers who bought just one pencil
= 1 u - 510
= 720 - 510
= 210

Answer(s): 210