Sam has twice as many books as Jim. If Sam gives 12 books to Jim, they will have the same number of books. How many books to they have altogether?
To solve this problem, let's break it down step by step:
1. Let's assume that Jim has x books.
2. Since Sam has twice as many books as Jim, he would have 2x books.
3. If Sam gives 12 books to Jim, Sam's new book count would be 2x - 12 (as he had 2x books).
4. Jim's new book count would be x + 12 (as he received 12 books from Sam).
5. Now, we know that after exchanging the books, Sam and Jim will have the same number of books. Therefore, we can set up an equation: 2x - 12 = x + 12.
6. Let's solve this equation to find x:
2x - 12 = x + 12
Subtract x from both sides:
x - 12 = 12
Add 12 to both sides:
x = 24
7. We have determined that Jim originally had 24 books.
8. Since Sam has twice as many books as Jim, he has 2 * 24 = 48 books.
9. Now, to find out the total number of books they have altogether, we simply add their individual book counts:
Jim's books + Sam's books = 24 + 48 = 72
10. Therefore, Sam and Jim have 72 books altogether.
So, Sam and Jim have a total of 72 books.
21
S = 2J
S - 12 = J + 12
Substitute 2J for S in the second equation and solve for J. Insert that value into the first equation to solve for S. Check by putting both values into the second equation. Add the two.