To find out how many beads Neil started with, we can set up an equation based on the information given. Let \( b \) be the initial number of beads Neil has.
- He makes 8 identical necklaces, which means he uses up \( \frac{b}{8} \) beads for each necklace.
- He then buys 25 beads at the store.
- After these operations, he ends up with a total of 500 beads.
We can express that in an equation:
\[ \frac{b}{8} + 25 = 500 \]
Now, let's rearrange this equation to isolate \( b \).
- First, subtract 25 from both sides:
\[ \frac{b}{8} = 500 - 25 \] \[ \frac{b}{8} = 475 \]
- Now, multiply both sides by 8 to solve for \( b \):
\[ b = 475 \times 8 \] \[ b = 3800 \]
Now, to identify the operations used in the original equation:
- The equation starts with a division ( \( b/8 \) ) and involves addition (adding 25).
- The manipulation to isolate \( b \) involves subtraction and multiplication.
Thus, the correct option that describes the operations used to solve this problem is:
a. subtraction and division (for the rearrangement) and d. addition and multiplication (for the operations described in the equation).
However, among the available choices, the primary operations in the equation itself are division and addition, which aligns with b. addition and division.
Therefore, the best answer is b. addition and division.