To find out how many kilograms of books should be transferred from crate B to crate A so that both crates weigh the same, we can set up the following equation:
Let \( x \) be the amount of books (in kg) to be taken out of crate B and put into crate A.
After transferring \( x \) kg from crate B to crate A:
- Weight of crate A: \( 56 + x \) kg
- Weight of crate B: \( 68 - x \) kg
We want these weights to be equal:
\[ 56 + x = 68 - x \]
Now, we can solve for \( x \):
- Add \( x \) to both sides:
\[ 56 + 2x = 68 \]
- Subtract 56 from both sides:
\[ 2x = 12 \]
- Divide both sides by 2:
\[ x = 6 \]
Thus, you should take out 6 kg of books from crate B and put them into crate A in order for both crates to weigh the same.
After the transfer, both crates will weigh:
- Crate A: \( 56 + 6 = 62 \) kg
- Crate B: \( 68 - 6 = 62 \) kg
So both crates will weigh 62 kg.