Luke bought some pencils at $4 each. He later sold them to his customers at $7 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Luke gave away 140 free pencils and collected a total of $880 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 - 420	420
Value	$4	$7	$7
Total Value	4 u	7 u - $2940	$1960

Since 140 pencils were given free, there were 140 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 140
= 420

Number of pencils for customers who each bought 1 pencil = 1 u - 420

Total amount collected from customers who bought 1 pencil each
= 7 x (1 u - 420)
= 7 u - 2940

Total amount collected from customers who bought two pencils each
= 140 x 2 x 7
= $1960

Total amount collected from all the customers
= 7 u - 2940 + 1960
= 7 u - 980

Luke collected a total of $880 more than what he had paid for.

7 u - 980 = 4 u + 880
7 u - 4 u = 880 + 980
3 u = 1860

1 u = 1860 ÷ 3 = 620

Number of customers who bought just one pencil
= 1 u - 420
= 620 - 420
= 200

Answer(s): 200