Question

Sam spent 1/2 of a sum of money on a book, and 1/2 of the remainder on a bag of candy. He had $2 left. How much did he pay for the book?

Answer 1

To find out how much Sam paid for the book, we need to follow several steps. Sam initially had 8 dollars and spent 4 dollars on the book.

Step-by-step explanation:

To find out how much Sam paid for the book, we need to follow these steps:

1. Let's assume the sum of money Sam had initially is 'x' dollars.
2. Sam spent 1/2 of the sum on a book, so he spent (1/2)x dollars on the book. The remaining amount is (1/2)x dollars.
3. Sam then spent 1/2 of the remainder on a bag of candy, so he spent (1/2)((1/2)x) = (1/4)x dollars on the bag of candy.
4. The total amount spent on the book and the bag of candy is ((1/2)x) + ((1/4)x) = (3/4)x dollars.
5. We are told that Sam had $2 left, so the remaining amount is (1/4)x = 2 dollars.
6. To find how much Sam paid for the book, we can solve for 'x' using the equation (1/4)x = 2.
7. Multiplying both sides of the equation by 4, we get x = 8.
8. Therefore, Sam initially had 8 dollars and spent (1/2)(8) = 4 dollars on the book.