Vincent bought some pencils at $3 each. He later sold them to his customers at $5 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Vincent gave away 230 free pencils and collected a total of $270 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 - 690	690
Value	$3	$5	$5
Total Value	3 u	5 u - $3450	$2300

Since 230 pencils were given free, there were 230 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 230
= 690

Number of pencils for customers who each bought 1 pencil = 1 u - 690

Total amount collected from customers who bought 1 pencil each
= 5 x (1 u - 690)
= 5 u - 3450

Total amount collected from customers who bought two pencils each
= 230 x 2 x 5
= $2300

Total amount collected from all the customers
= 5 u - 3450 + 2300
= 5 u - 1150

Vincent collected a total of $270 more than what he had paid for.

5 u - 1150 = 3 u + 270
5 u - 3 u = 270 + 1150
2 u = 1420

1 u = 1420 ÷ 2 = 710

Number of customers who bought just one pencil
= 1 u - 690
= 710 - 690
= 20

Answer(s): 20