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)

Question

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.