David bought some staplers at $5 each. He later sold them to his customers at $7 each. For customers who bought two staplers were given another stapler for free. The customers bought either one or two staplers. David gave away 140 free staplers and collected a total of $540 more than what he had paid for. How many customers bought just one stapler each?
|
Staplers sold |
Staplers given to customers who got 1 stapler each |
Staplers given to customers who got 3 staplers each |
Number |
1 u |
1 u - 420 |
420 |
Value |
$5 |
$7 |
$7 |
Total Value |
5 u |
7 u - $2940 |
$1960 |
Since 140 staplers were given free, there were 140 customers who bought two staplers each.
Number of staplers that each customer would get if they bought two staplers each and got 1 stapler free
= 2 + 1
= 3
Total number of staplers for customers who each bought two staplers
= 3 x 140
= 420
Number of staplers for customers who each bought 1 stapler = 1 u - 420
Total amount collected from customers who bought 1 stapler each
= 7 x (1 u - 420)
= 7 u - 2940
Total amount collected from customers who bought two staplers each
= 140 x 2 x 7
= $1960
Total amount collected from all the customers
= 7 u - 2940 + 1960
= 7 u - 980
David collected a total of $540 more than what he had paid for.
7 u - 980 = 5 u + 540
7 u - 5 u = 540 + 980
2 u = 1520
1 u = 1520 ÷ 2 = 760
Number of customers who bought just one stapler
= 1 u - 420
= 760 - 420
= 340
Answer(s): 340