Tom bought some pencils at $3 each. He later sold them to his customers at $6 each. For customers who bought two pencils were given another pencil for free. The customers bought either one or two pencils. Tom gave away 140 free pencils and collected a total of $1530 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 - 420 |
420 |
| Value |
$3 |
$6 |
$6 |
| Total Value |
3 u |
6 u - $2520 |
$1680 |
Since 140 pencils were given free, there were 140 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 140
= 420
Number of pencils for customers who each bought 1 pencil = 1 u - 420
Total amount collected from customers who bought 1 pencil each
= 6 x (1 u - 420)
= 6 u - 2520
Total amount collected from customers who bought two pencils each
= 140 x 2 x 6
= $1680
Total amount collected from all the customers
= 6 u - 2520 + 1680
= 6 u - 840
Tom collected a total of $1530 more than what he had paid for.
6 u - 840 = 3 u + 1530
6 u - 3 u = 1530 + 840
3 u = 2370
1 u = 2370 ÷ 3 = 790
Number of customers who bought just one pencil
= 1 u - 420
= 790 - 420
= 370
Answer(s): 370
