Niel has a bucket of beads. He uses them to make 8 identical necklaces and then buys 25 beads at the store. He ends up with a total of 500 beads. How many did he start with? Identify the operations needed to solve this problem using the equation b8 + 25 = 500

Answer 1

To solve the problem, let's first break down the equation given:

\[ b \times 8 + 25 = 500 \]

where \( b \) represents the number of beads used for each necklace.

Operations Needed:

1. Multiply: The term \( b \times 8 \) represents the total number of beads Niel used to make the 8 identical necklaces. Therefore, to find the total number of beads used for the necklaces, you multiply the number of beads for one necklace by 8.

2. Add: The \( + 25 \) accounts for the additional 25 beads that Niel bought at the store.

3. Subtract: To find out how many beads he started with, you will subtract the 25 beads he bought from the total of 500 beads. This will give you the total number of beads he originally had before buying more.

Steps to Solve for \( b \):

1. Subtract 25 from both sides: \[ b \times 8 = 500 - 25 \]

2. Calculate: \[ b \times 8 = 475 \]

3. Divide by 8: \[ b = \frac{475}{8} \]

Thus, the number of beads per necklace can be calculated.

4. To find the total number of beads he started with, multiply \( b \) by 8 and then add 25: \[ \text{Total beads started with} = (b \times 8) + 25 = 475 + 25 = 500 \]

Therefore, to get the original number of beads, you need to compute: \[ \text{Original beads} = 475 (the number used for 8 necklaces) + 25 (the beads bought) = 500. \]

Final Calculation:

Now, calculating \( b \) gives approximately: \[ b = 59.375 \] As this does not work in the context of a number of beads, you can conclude that he used 59 beads for each necklace (assuming whole beads).

Conclusion:

He started with \( 475 \) beads total (not including the 25 he bought). So Niel started with:

\[ 500 - 25 = 475 \text{ beads.} \]

In summary, Niel started with 475 beads.