Brandon bought some pencils at $6 each. He later sold them to his customers at $8 each. For customers who bought four pencils were given another pencil for free. The customers bought either one or four pencils. Brandon gave away 100 free pencils and collected a total of $660 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 5 pencils each |
Number |
1 u |
1 u - 500 |
500 |
Value |
$6 |
$8 |
$8 |
Total Value |
6 u |
8 u - $4000 |
$3200 |
Since 100 pencils were given free, there were 100 customers who bought four pencils each.
Number of pencils that each customer would get if they bought four pencils each and got 1 pencil free
= 4 + 1
= 5
Total number of pencils for customers who each bought four pencils
= 5 x 100
= 500
Number of pencils for customers who each bought 1 pencil = 1 u - 500
Total amount collected from customers who bought 1 pencil each
= 8 x (1 u - 500)
= 8 u - 4000
Total amount collected from customers who bought four pencils each
= 100 x 4 x 8
= $3200
Total amount collected from all the customers
= 8 u - 4000 + 3200
= 8 u - 800
Brandon collected a total of $660 more than what he had paid for.
8 u - 800 = 6 u + 660
8 u - 6 u = 660 + 800
2 u = 1460
1 u = 1460 ÷ 2 = 730
Number of customers who bought just one pencil
= 1 u - 500
= 730 - 500
= 230
Answer(s): 230