Brandon bought some pencils at $6 each. He later sold them to his customers at $11 each. For customers who bought three pencils were given another pencil for free. The customers bought either one or three pencils. Brandon gave away 120 free pencils and collected a total of $2080 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 - 480 |
480 |
| Value |
$6 |
$11 |
$11 |
| Total Value |
6 u |
11 u - $5280 |
$3960 |
Since 120 pencils were given free, there were 120 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 120
= 480
Number of pencils for customers who each bought 1 pencil = 1 u - 480
Total amount collected from customers who bought 1 pencil each
= 11 x (1 u - 480)
= 11 u - 5280
Total amount collected from customers who bought three pencils each
= 120 x 3 x 11
= $3960
Total amount collected from all the customers
= 11 u - 5280 + 3960
= 11 u - 1320
Brandon collected a total of $2080 more than what he had paid for.
11 u - 1320 = 6 u + 2080
11 u - 6 u = 2080 + 1320
5 u = 3400
1 u = 3400 ÷ 5 = 680
Number of customers who bought just one pencil
= 1 u - 480
= 680 - 480
= 200
Answer(s): 200
