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 b/8 + 25 = 500.
subtraction and division
addition and multiplication
subtraction and multiplication
addition and division
addition and division
The operations needed to solve this problem using the equation b/8 + 25 = 500 are subtraction and multiplication. Here's how you can use these operations to find the solution:
1. The variable "b" represents the number of beads that Niel started with. We need to find this value.
2. The equation b/8 + 25 = 500 can be rearranged to isolate the variable b. Begin by subtracting 25 from both sides of the equation: b/8 = 500 - 25.
3. Simplifying the right-hand side of the equation gives us: b/8 = 475.
4. To get the value of b, we need to undo the division by 8. Multiply both sides of the equation by 8: (8 * b) / 8 = 475 * 8.
5. On the left-hand side, the 8s cancel out, leaving just b: b = 475 * 8.
6. Finally, multiply 475 by 8 to get the value of b: b = 3800.
Therefore, Niel started with 3,800 beads.
The correct operations needed to solve this problem using the equation b/8 + 25 = 500 are addition and multiplication.
Explanation:
Let's break down the equation step by step and identify the operations required:
1. The variable b represents the number of beads Niel started with.
2. He used the beads to make 8 identical necklaces. Thus, the number of beads in each necklace would be b/8.
3. Adding 25 more beads, the total number of beads Niel has now is (b/8) + 25.
4. According to the problem, the total number of beads is 500. So we can set up the equation: (b/8) + 25 = 500.
5. To solve this equation, the first operation needed is addition to combine the two terms on the left side: (b/8) + 25.
6. The next operation needed is multiplication. We multiply 8 by (b/8) to cancel out 8 in the denominator: (8/1) * (b/8).
7. Finally, by multiplying 8 by (b/8), it cancels out and we are left with b: b + (25 * 8/1) = 500.
Therefore, the correct operations needed to solve the problem using the equation b/8 + 25 = 500 are addition and multiplication.