Suppose that a bookstore buys a textbook from the publisher for $50. At what price should the bookstore mark the textbook so that it may be offered at a discount of 20% but still give the bookstore a 40% profit on the $50 investment?

To obtain the desired 40% profit,
the book needs to sell for $50 + 40% * $50
Our target price for the sale is 50 + 0.4*50
= 50 + 20
=$70
We need the original price of the book
to be enough so that 20% off of that
price gives us $70

Set P = the original price
The original price minus 20% of the original price must equal $70
P - 20% * P = 70
P - 0.20P = 70
0.80P = 70
Divide each side by 0.80
P = 70/0.80
P = 87.5
So the books original price needs to be $87.5