Fred bought some pencils at $6 each. He later sold them to his customers at $9 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Fred gave away 180 free pencils and collected a total of $30 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 - 540 |
540 |
| Value |
$6 |
$9 |
$9 |
| Total Value |
6 u |
9 u - $4860 |
$3240 |
Since 180 pencils were given free, there were 180 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 180
= 540
Number of pencils for customers who each bought 1 pencil = 1 u - 540
Total amount collected from customers who bought 1 pencil each
= 9 x (1 u - 540)
= 9 u - 4860
Total amount collected from customers who bought two pencils each
= 180 x 2 x 9
= $3240
Total amount collected from all the customers
= 9 u - 4860 + 3240
= 9 u - 1620
Fred collected a total of $30 more than what he had paid for.
9 u - 1620 = 6 u + 30
9 u - 6 u = 30 + 1620
3 u = 1650
1 u = 1650 ÷ 3 = 550
Number of customers who bought just one pencil
= 1 u - 540
= 550 - 540
= 10
Answer(s): 10
