Jack bought some pencils at $6 each. He later sold them to his customers at $11 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Jack gave away 240 free pencils and collected a total of $1110 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 - 720 |
720 |
Value |
$6 |
$11 |
$11 |
Total Value |
6 u |
11 u - $7920 |
$5280 |
Since 240 pencils were given free, there were 240 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 240
= 720
Number of pencils for customers who each bought 1 pencil = 1 u - 720
Total amount collected from customers who bought 1 pencil each
= 11 x (1 u - 720)
= 11 u - 7920
Total amount collected from customers who bought two pencils each
= 240 x 2 x 11
= $5280
Total amount collected from all the customers
= 11 u - 7920 + 5280
= 11 u - 2640
Jack collected a total of $1110 more than what he had paid for.
11 u - 2640 = 6 u + 1110
11 u - 6 u = 1110 + 2640
5 u = 3750
1 u = 3750 ÷ 5 = 750
Number of customers who bought just one pencil
= 1 u - 720
= 750 - 720
= 30
Answer(s): 30