Elijah bought some pencils at $6 each. He later sold them to his customers at $11 each. For customers who bought four pencils were given another pencil for free. The customers bought either one or four pencils. Elijah gave away 130 free pencils and collected a total of $2420 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 - 650 |
650 |
| Value |
$6 |
$11 |
$11 |
| Total Value |
6 u |
11 u - $7150 |
$5720 |
Since 130 pencils were given free, there were 130 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 130
= 650
Number of pencils for customers who each bought 1 pencil = 1 u - 650
Total amount collected from customers who bought 1 pencil each
= 11 x (1 u - 650)
= 11 u - 7150
Total amount collected from customers who bought four pencils each
= 130 x 4 x 11
= $5720
Total amount collected from all the customers
= 11 u - 7150 + 5720
= 11 u - 1430
Elijah collected a total of $2420 more than what he had paid for.
11 u - 1430 = 6 u + 2420
11 u - 6 u = 2420 + 1430
5 u = 3850
1 u = 3850 ÷ 5 = 770
Number of customers who bought just one pencil
= 1 u - 650
= 770 - 650
= 120
Answer(s): 120
