Dylan 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. Dylan gave away 170 free pencils and collected a total of $2410 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 - 680	680
Value	$2	$7	$7
Total Value	2 u	7 u - $4760	$3570

Since 170 pencils were given free, there were 170 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 170
= 680

Number of pencils for customers who each bought 1 pencil = 1 u - 680

Total amount collected from customers who bought 1 pencil each
= 7 x (1 u - 680)
= 7 u - 4760

Total amount collected from customers who bought three pencils each
= 170 x 3 x 7
= $3570

Total amount collected from all the customers
= 7 u - 4760 + 3570
= 7 u - 1190

Dylan collected a total of $2410 more than what he had paid for.

7 u - 1190 = 2 u + 2410
7 u - 2 u = 2410 + 1190
5 u = 3600

1 u = 3600 ÷ 5 = 720

Number of customers who bought just one pencil
= 1 u - 680
= 720 - 680
= 40

Answer(s): 40