Rajan bought 5 copies of a book to give as gifts. The book was on sale for $5 off the
original price. The total that Rajan spent on 5 books was $2 more than he would have
spent on 4 copies of the book at the original price. What was the original price?

The original price of the book is $27

Step-by-step explanation:

Assume that the original price of each book is $x

∵ The book was on sale for $5 off of the  original price

∵ The original price is $x

- To find the price on sale subtract 5 from x

∴ The price on sale = x - 5

∵ He bought 5 copies on the sale

∴ The total price of them = 5(x - 5)

∵ The total that he spent on 5 books was $2 more than he

   would have  spent on 4 copies of the book at the original price

∵ The price of the 4 copies = 4 x

- Subtract 4 x from the price on sale and equate the difference by 2

∴ 5(x - 5) - 4 x = 2

- Simplify the left hand side

∴ 5 x - 25 - 4 x = 2

- Add the like term

∴ x - 25 = 2

- Add 25 to both sides

∴ x = 27

∵ x is the original price of each book

∴ The original price of the book is $27

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.