To determine which graph represents the number of bracelets and necklaces Sharon can make with her 1000 beads, we first need to establish the relationship between the number of bracelets (B) and necklaces (N) she can create using the beads.
1. Set Up the Equation
Each necklace requires 40 beads, and each bracelet requires 20 beads. Sharon has a total of 1000 beads.
The relationship can be expressed as: \[ 40N + 20B \leq 1000 \]
2. Simplifying the Equation
To make this simpler, we can divide the entire equation by 20: \[ 2N + B \leq 50 \]
3. Graphing the Equation
To graph this inequality, we need to find the intercepts:
- When \(N = 0\): \[ B = 50 \quad (the B-intercept) \]
- When \(B = 0\): \[ 2N = 50 \implies N = 25 \quad (the N-intercept) \]
4. Plotting the Points
- The B-intercept is at (50, 0)
- The N-intercept is at (0, 25)
5. Linearity
The line represented by the equation \(2N + B = 50\) will have a slope of -2 (since for every additional necklace, the number of bracelets decreases by 2).
6. Identifying the Correct Graph
With the intercepts and the relationship in mind, we can identify the graph that shows:
- The line from the point (50, 0) to (0, 25)
- The area under and including this line because it represents the combinations of bracelets and necklaces that can be made within the total bead limit.
Conclusion
Without seeing the actual graphs, we cannot definitively choose one, but you should look for:
- A line running from (50, 0) to (0, 25)
- An area that includes combinations below this line.
Once you identify that, you can choose the graph that corresponds to this relationship. If you have images or descriptions of graphs J, K, L, or M, you can identify which one matches the plotting described.
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