Question

After purchasing a book that has a no return policy , the book goes on sale at the bookstore for 15% less . You realize that you spent an extra $12.75 on the book . What amount did you pay for the book originally ?

Answer 1

To determine the original price of the book, we set up an equation where x represents the original price, and solve for x knowing the sale price is 15% less. The equation 0.85x = x - $12.75 results from the sale discount, which simplifies to x = $85.00 as the original price of the book.

Step-by-step explanation:

The student asks how to calculate the original price of a book before it went on sale, given that they spent an extra $12.75 because it was later discounted by 15%. To solve this problem, we define the original price as 'x'. Since the book was later sold for 15% less, we know that 85% of the original price is the sale price (100% - 15% = 85%). The sale price can be expressed as 0.85x.

The student spent an extra $12.75 on the book, which means the difference between the original price and the sale price is $12.75. Hence, we have the equation 0.85x = x - $12.75. We are looking for the value of x.

To find x, we can reorganize the equation: x - 0.85x = $12.75 => 0.15x = $12.75. Dividing both sides of the equation by 0.15, we find x = $12.75 / 0.15, which gives us the original price x = $85.00.

Therefore, the original price paid for the book was $85.00.