Vaidev bought some pens at $3 each. He later sold them to his customers at $7 each. For customers who bought three pens were given another pen for free. The customers bought either one or three pens. Vaidev gave away 110 free pens and collected a total of $1230 more than what he had paid for. How many customers bought just one pen each?
| |
Pens
sold |
Pens given to customers who got 1 pen each |
Pens given to customers who got 4 pens each |
| Number |
1 u |
1 u - 440 |
440 |
| Value |
$3 |
$7 |
$7 |
| Total Value |
3 u |
7 u - $3080 |
$2310 |
Since 110 pens were given free, there were 110 customers who bought three pens each.
Number of pens that each customer would get if they bought three pens each and got 1 pen free
= 3 + 1
= 4
Total number of pens for customers who each bought three pens
= 4 x 110
= 440
Number of pens for customers who each bought 1 pen = 1 u - 440
Total amount collected from customers who bought 1 pen each
= 7 x (1 u - 440)
= 7 u - 3080
Total amount collected from customers who bought three pens each
= 110 x 3 x 7
= $2310
Total amount collected from all the customers
= 7 u - 3080 + 2310
= 7 u - 770
Vaidev collected a total of $1230 more than what he had paid for.
7 u - 770 = 3 u + 1230
7 u - 3 u = 1230 + 770
4 u = 2000
1 u = 2000 ÷ 4 = 500
Number of customers who bought just one pen
= 1 u - 440
= 500 - 440
= 60
Answer(s): 60
