Liam is selling 900 colouring books. He sold 50% of them at $10 each, 30% of the remainder at a discount of 20% and the rest at cost price. He made a profit of $2246. Find the cost price of a colouring book.
| Price |
$10 |
$8 |
Cost Price |
| Percent |
50% |
50% |
| |
|
15% |
35% |
| Number |
450 |
135 |
Not needed |
| Amount collected |
$4500 |
$1080 |
Not needed |
Number of colouring books sold at $10
= 50% x 900
=
50100 x 900
= 450
Price after 20% discount
= 80% x 10
=
80100 x 10
= $8
Remaining colouring books
= 900 - 450
= 450
Number of colouring books sold at $8
= 30% x 450
=
30100 x 450
= 135
Number of colouring books sold at $10 or 20% discount
= 450 + 135
= 585
Total amount collected from the sale of 450 colouring books
= 450 x 10
= $4500
Total amount collected from the sale of the other 135 colouring books
= 135 x 8
= $1080
Total amount collected from the sale of colouring books sold at $10 or 20% discount
= 4500 + 1080
= $5580
Cost price of 585 colouring books
= 5580 - 2246
= $4680
Cost price of 1 colouring book
= 4680 ÷ 585
= $8
Answer(s): $8
