To solve the problem, we need to express how many beads Niel started with using the given information.
Let's define \( b \) as the number of beads Niel started with. The problem states that he makes 8 identical necklaces, and we can infer that he uses a certain number of beads for each necklace. We also know he buys 25 additional beads after making the necklaces, and in the end, he has a total of 500 beads.
The equation you provided is \( \frac{b}{8} + 25 = 500 \).
However, this equation appears to have a slight misunderstanding. The equation should represent the total of the beads after Niel made the necklaces and then bought more beads.
Let’s clarify the equation:
- Niel starts with \( b \) beads.
- He makes 8 necklaces. If we assume he uses all the beads to make the necklaces evenly, we need his bead count before necklaces to see how many he used for each necklace.
This situation doesn't directly match with \( \frac{b}{8} \). Niel uses a certain number of beads for each necklace, and this is not directly visible in the provided equation. Let’s reframe it correctly:
The operation should go as follows:
- Niel initially had \( b \) beads.
- He buys 25 beads.
- After making the necklaces, he ends up with 500 beads.
So, the correct operation regarding beads before making necklaces could be \( b - x + 25 = 500 \), where \( x \) is the number of beads used to make the necklaces.
Assuming \( x \) can be calculated, if he made 8 necklaces, assuming equal distribution \( x = \text{ beads used to make necklaces} \). If he used \( \frac{b}{n} \) for each necklace (which can imply Niel used some beads; however, without a specific number of beads used per necklaces, we cannot derive exact value).
To solve it:
- Rearranging the equation correctly allows us to derive for \( b \).
- From our assumption, regroup the given:
- If he ends with 500 after he started with \( b \):
- \( b - x + 25 = 500 \).
- Hence, \( b - x = 475 \) (requires clarity on what ‘x’ is).
However, you can continue by calculating based on values provided to derive \( b \). If we assume he doesn’t use beads in strings, simply \( b + 25 = 500 \) then implies he started with \( 475 \) beads.
Lastly, clarify the number of beads used to confirm your necklace assembly.