Neil 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 = 500b8 + 25 = 500 .
To solve this problem, we need to use the equation b * 8 + 25 = 500, where b represents the number of beads Neil started with.
Here are the operations needed to solve this equation:
1. Multiply the number of beads Neil started with (b) by 8 to represent the 8 necklaces he made: 8b.
2. Add 25 beads he bought at the store to the number of beads Neil started with: 8b + 25.
3. Set this sum equal to 500, the total number of beads he ended up with: 8b + 25 = 500.
To find the value of b, we can now solve this equation.
To solve this problem, we need to set up an equation using the given information.
Let's assume that Neil started with "x" number of beads.
Neil uses these beads to make 8 identical necklaces. Each necklace requires the same number of beads. So, the number of beads used for each necklace can be expressed as x/8.
After making the necklaces, Neil buys an additional 25 beads from the store.
So, the total number of beads Neil has can be represented as:
x/8 + 25 = 500
To find the value of "x," we need to solve this equation.
1. First, we'll simplify the equation by multiplying both sides by 8 to eliminate the fraction:
8 * (x/8 + 25) = 8 * 500
Simplifying further:
x + 200 = 4000
2. Next, we'll isolate the variable by subtracting 200 from both sides of the equation:
x + 200 - 200 = 4000 - 200
Simplifying further:
x = 3800
Therefore, Neil initially started with 3800 beads.
To solve this problem, we can use the equation:
Number of beads originally + Number of beads bought = Total number of beads
Let's assign a variable to the number of beads originally:
Let b represent the number of beads Neil originally had.
According to the problem, Neil uses his beads to make 8 identical necklaces and then buys 25 more beads. So, we can set up the equation:
b * 8 + 25 = 500
To find the original number of beads (b), we need to isolate it on one side of the equation.
First, distribute 8 to b:
8b + 25 = 500
Next, subtract 25 from both sides to isolate the variable term:
8b = 500 - 25
Simplifying:
8b = 475
Finally, divide both sides by 8 to solve for b:
b = 475 / 8
Now we can determine the value of b by performing the division:
b ≈ 59.375
Since Neil can't have a fraction of a bead, we need to round this answer to the nearest whole number. Therefore, Neil started with approximately 59 beads.