The price of an antique book is $91, which is two-fifth more then the cost to the book dealer. Find the cost.

Let the price of book x. That's the cost the book dealer.

He wants to earn some money while selling it, so he listed the book by a new price, 91 $

He added two-fifth (2/5) price to its initial price. In other words, its new price is 40 % more expensive. (2/5 = x / 100)

Here is the equation in words,

initial price + 2/5 of the initial price = 91

by equation: x + 2/5 x = 91

multiply both sides by 5, to eliminate the denominator:

5x + 2x = 91.5; 7x = 455

divide both sides by 7 to simply coefficient of x: x = 65

The answer is 65$.