Valen bought some pens at $5 each. He later sold them to his customers at $7 each. For customers who bought two pens were given another pen for free. The customers bought either one or two pens. Valen gave away 150 free pens and collected a total of $210 more than what he had paid for. How many customers bought just one pen each?

	Pens sold	Pens given to customers who got 1 pen each	Pens given to customers who got 3 pens each
Number	1 u	1 u - 450	450
Value	$5	$7	$7
Total Value	5 u	7 u - $3150	$2100

Since 150 pens were given free, there were 150 customers who bought two pens each.

Number of pens that each customer would get if they bought two pens each and got 1 pen free
= 2 + 1
= 3

Total number of pens for customers who each bought two pens 
= 3 x 150
= 450

Number of pens for customers who each bought 1 pen = 1 u - 450

Total amount collected from customers who bought 1 pen each
= 7 x (1 u - 450)
= 7 u - 3150

Total amount collected from customers who bought two pens each
= 150 x 2 x 7
= $2100

Total amount collected from all the customers
= 7 u - 3150 + 2100
= 7 u - 1050

Valen collected a total of $210 more than what he had paid for.

7 u - 1050 = 5 u + 210
7 u - 5 u = 210 + 1050
2 u = 1260

1 u = 1260 ÷ 2 = 630

Number of customers who bought just one pen
= 1 u - 450
= 630 - 450
= 180

Answer(s): 180