Rael bought some pencils at $4 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. Rael gave away 160 free pencils and collected a total of $1190 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 - 640	640
Value	$4	$7	$7
Total Value	4 u	7 u - $4480	$3360

Since 160 pencils were given free, there were 160 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 160
= 640

Number of pencils for customers who each bought 1 pencil = 1 u - 640

Total amount collected from customers who bought 1 pencil each
= 7 x (1 u - 640)
= 7 u - 4480

Total amount collected from customers who bought three pencils each
= 160 x 3 x 7
= $3360

Total amount collected from all the customers
= 7 u - 4480 + 3360
= 7 u - 1120

Rael collected a total of $1190 more than what he had paid for.

7 u - 1120 = 4 u + 1190
7 u - 4 u = 1190 + 1120
3 u = 2310

1 u = 2310 ÷ 3 = 770

Number of customers who bought just one pencil
= 1 u - 640
= 770 - 640
= 130

Answer(s): 130