Question

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.(1 point)
Responses

addition and multiplication
addition and multiplication

subtraction and division
subtraction and division

addition and division
addition and division

subtraction and multiplication

Answer 1

To solve the problem, let's begin by analyzing the equation given:

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

Here, \( b \) represents the number of beads Niel started with.

The operations involved are:
1. **Multiplication (b \cdot 8)**: This is used to determine the total number of beads used to make the 8 necklaces.
2. **Addition (+ 25)**: This operation is used to account for the 25 beads Niel bought after making the necklaces.
3. **Subtraction** is needed to isolate \( b \) after we have obtained the sum of beads used and the ones bought.
4. **Division** would come into play if we were determining how many beads were on each necklace after finding \( b \).

However, to directly identify how many beads he started with based on the equation provided, the relevant operations used in the solving process after writing the equation would be:

1. First, you would subtract 25 from both sides to isolate the term with \( b \):
\[
b \cdot 8 = 500 - 25
\]
2. Then, you would divide both sides by 8 to solve for \( b \):
\[
b = \frac{475}{8}
\]

Considering the main operations used to solve the equation:

- The equation involves **addition** (for the beads bought) and **division** (to find out how many beads were initially present based on how many were used per necklace).

Therefore, the correct response is:

**Addition and Division**.