Liam is selling 900 guide books. He sold 75% of them at $5 each, 40% of the remainder at a discount of 40% and the rest at cost price. He made a profit of $2282. Find the cost price of a guide book.
| Price |
$5 |
$3 |
Cost Price |
| Percent |
75% |
25% |
| |
|
10% |
15% |
| Number |
675 |
90 |
Not needed |
| Amount collected |
$3375 |
$270 |
Not needed |
Number of guide books sold at $5
= 75% x 900
=
75100 x 900
= 675
Price after 40% discount
= 60% x 5
=
60100 x 5
= $3
Remaining guide books
= 900 - 675
= 225
Number of guide books sold at $3
= 40% x 225
=
40100 x 225
= 90
Number of guide books sold at $5 or 40% discount
= 675 + 90
= 765
Total amount collected from the sale of 675 guide books
= 675 x 5
= $3375
Total amount collected from the sale of the other 90 guide books
= 90 x 3
= $270
Total amount collected from the sale of guide books sold at $5 or 40% discount
= 3375 + 270
= $3645
Cost price of 765 guide books
= 3645 - 2282
= $7650
Cost price of 1 guide book
= 7650 ÷ 765
= $10
Answer(s): $10
