Vincent bought some pencils at $2 each. He later sold them to his customers at $7 each. For customers who bought three pencils were given another pencil for free. The customers bought either one or three pencils. Vincent gave away 110 free pencils and collected a total of $2730 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 - 440	440
Value	$2	$7	$7
Total Value	2 u	7 u - $3080	$2310

Since 110 pencils were given free, there were 110 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 110
= 440

Number of pencils for customers who each bought 1 pencil = 1 u - 440

Total amount collected from customers who bought 1 pencil each
= 7 x (1 u - 440)
= 7 u - 3080

Total amount collected from customers who bought three pencils each
= 110 x 3 x 7
= $2310

Total amount collected from all the customers
= 7 u - 3080 + 2310
= 7 u - 770

Vincent collected a total of $2730 more than what he had paid for.

7 u - 770 = 2 u + 2730
7 u - 2 u = 2730 + 770
5 u = 3500

1 u = 3500 ÷ 5 = 700

Number of customers who bought just one pencil
= 1 u - 440
= 700 - 440
= 260

Answer(s): 260