Perry bought some pencils at $4 each. He later sold them to his customers at $9 each. For customers who bought four pencils were given another pencil for free. The customers bought either one or four pencils. Perry gave away 140 free pencils and collected a total of $2640 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 - 700 |
700 |
| Value |
$4 |
$9 |
$9 |
| Total Value |
4 u |
9 u - $6300 |
$5040 |
Since 140 pencils were given free, there were 140 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 140
= 700
Number of pencils for customers who each bought 1 pencil = 1 u - 700
Total amount collected from customers who bought 1 pencil each
= 9 x (1 u - 700)
= 9 u - 6300
Total amount collected from customers who bought four pencils each
= 140 x 4 x 9
= $5040
Total amount collected from all the customers
= 9 u - 6300 + 5040
= 9 u - 1260
Perry collected a total of $2640 more than what he had paid for.
9 u - 1260 = 4 u + 2640
9 u - 4 u = 2640 + 1260
5 u = 3900
1 u = 3900 ÷ 5 = 780
Number of customers who bought just one pencil
= 1 u - 700
= 780 - 700
= 80
Answer(s): 80
