Let's break down the given problem step by step in order to determine the correct equation that represents how many rocks George initially had.
1. Understanding the Problem:
- George acquires 5 new rocks and then gives half of his collection to Susan.
- Susan receives 36 rocks.
- We need to determine how many rocks George started with before acquiring the 5 new rocks.
2. Define the Variables:
- Let [tex]\( x \)[/tex] represent the initial number of rocks George had.
3. Form the Equation:
- After acquiring 5 new rocks, George's total number of rocks becomes [tex]\( x + 5 \)[/tex].
- The problem states that half of George's collection after getting the new rocks is given to Susan. Therefore, half of [tex]\( x + 5 \)[/tex] is equal to 36 rocks.
4. Set Up the Equation:
- The mathematical representation of giving half of the rocks would be:
[tex]\[
\frac{1}{2}(x + 5) = 36
\][/tex]
We can double-check that this equation represents the situation correctly:
- After getting 5 new rocks, George's collection: [tex]\( x + 5 \)[/tex]
- Giving half of this collection to Susan: [tex]\( \frac{1}{2}(x + 5) \)[/tex]
- Number of rocks Susan receives: 36
Thus, the equation that correctly matches this scenario is:
[tex]\[
\frac{1}{2}(x + 5) = 36
\][/tex]
So, the correct equation to determine how many rocks George started with is:
[tex]\(\boxed{\frac{1}{2}(x+5)=36}\)[/tex]
