Elijah bought some pencils at $5 each. He later sold them to his customers at $7 each. For customers who bought three pencils were given another pencil for free. The customers bought either one or three pencils. Elijah gave away 150 free pencils and collected a total of $250 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 - 600 |
600 |
Value |
$5 |
$7 |
$7 |
Total Value |
5 u |
7 u - $4200 |
$3150 |
Since 150 pencils were given free, there were 150 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 150
= 600
Number of pencils for customers who each bought 1 pencil = 1 u - 600
Total amount collected from customers who bought 1 pencil each
= 7 x (1 u - 600)
= 7 u - 4200
Total amount collected from customers who bought three pencils each
= 150 x 3 x 7
= $3150
Total amount collected from all the customers
= 7 u - 4200 + 3150
= 7 u - 1050
Elijah collected a total of $250 more than what he had paid for.
7 u - 1050 = 5 u + 250
7 u - 5 u = 250 + 1050
2 u = 1300
1 u = 1300 ÷ 2 = 650
Number of customers who bought just one pencil
= 1 u - 600
= 650 - 600
= 50
Answer(s): 50