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
A subtraction and division
B addition and division
C addition and multiplication
D subtraction and multiplication
B addition and division
The correct answer is option B: addition and division.
To solve this problem using the equation b/8 + 25 = 500, we need to use addition to combine two quantities and division to determine the original number of beads Niel started with (represented by 'b').
Step-by-step solution:
1. Start with the equation: b/8 + 25 = 500.
2. To solve for 'b', we need to isolate it on one side of the equation.
3. Subtract 25 from both sides of the equation: b/8 = 500 - 25.
4. Simplify the right side of the equation: b/8 = 475.
5. To solve for 'b', we need to isolate it. Since 'b' is divided by 8, we can multiply both sides of the equation by 8: 8 × (b/8) = 8 × 475.
6. Simplify the left side of the equation: b = 8 × 475.
7. Calculate the right side of the equation: b = 3800.
So, Niel started with 3800 beads.
To solve this problem using the equation b/8 + 25 = 500, we need to use addition and division operations.
First, let's break down the equation to understand what it represents:
b/8 + 25 = 500
The variable "b" represents the number of beads Niel started with. He then divides it by 8 to make 8 identical necklaces. After that, he buys 25 more beads, resulting in a total of 500 beads.
To find the initial number of beads Niel started with, we need to isolate the variable "b" on one side of the equation. Here's how we can do that:
1. Subtract 25 from both sides of the equation:
b/8 = 500 - 25
After performing the subtraction, the equation becomes:
b/8 = 475
2. To further isolate "b," we need to undo the division by 8. We can do this by multiplying both sides of the equation by 8:
8 * (b/8) = 8 * 475
The left side simplifies to just "b":
b = 8 * 475
Lastly, we multiply 8 by 475 to find the initial number of beads Niel started with:
b = 3800
Therefore, Niel started with 3800 beads.