Peter is selling 900 textbooks. He sold 50% of them at $5 each, 20% of the remainder at a discount of 20% and the rest at cost price. He made a profit of $2224. Find the cost price of a textbook.
| Price |
$5 |
$4 |
Cost Price |
| Percent |
50% |
50% |
| |
|
10% |
40% |
| Number |
450 |
90 |
Not needed |
| Amount collected |
$2250 |
$360 |
Not needed |
Number of textbooks sold at $5
= 50% x 900
=
50100 x 900
= 450
Price after 20% discount
= 80% x 5
=
80100 x 5
= $4
Remaining textbooks
= 900 - 450
= 450
Number of textbooks sold at $4
= 20% x 450
=
20100 x 450
= 90
Number of textbooks sold at $5 or 20% discount
= 450 + 90
= 540
Total amount collected from the sale of 450 textbooks
= 450 x 5
= $2250
Total amount collected from the sale of the other 90 textbooks
= 90 x 4
= $360
Total amount collected from the sale of textbooks sold at $5 or 20% discount
= 2250 + 360
= $2610
Cost price of 540 textbooks
= 2610 - 2224
= $5940
Cost price of 1 textbook
= 5940 ÷ 540
= $11
Answer(s): $11
