To determine which graph represents the number of bracelets and necklaces Sharon can make with 1000 beads, we first need to find the relationship between the number of bracelets (let's denote it as \( b \)) and the number of necklaces (let's denote it as \( n \)) she can create.
Each bracelet uses 20 beads, and each necklace uses 40 beads. Therefore, the total number of beads used can be expressed with the equation:
\[ 20b + 40n \leq 1000 \]
To simplify this equation, we can divide everything by 20:
\[ b + 2n \leq 50 \]
This equation describes a line in the \( b \)-\( n \) coordinate plane, where \( b \) represents the number of bracelets and \( n \) represents the number of necklaces. The intercepts of this equation can be found as follows:
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If \( n = 0 \): \[ b + 2(0) = 50 \implies b = 50 \] This gives the point (50, 0).
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If \( b = 0 \): \[ 0 + 2n = 50 \implies n = 25 \] This gives the point (0, 25).
The graph will have the line connecting these two points: (50, 0) and (0, 25). It will represent all combinations of bracelets and necklaces that Sharon can make without exceeding 1000 beads.
To find the proper graph among J, K, L, and M, you would look for a graph that:
- Has a line with a negative slope: This occurs since an increase in bracelets decreases the maximum number of necklaces (and vice versa).
- Intercepts are at (50, 0) for bracelets and (0, 25) for necklaces.
Once you identify the graph that meets these characteristics, that will be your answer. If you provide me with the details or a description of the graphs, I can help identify the correct one!
1 answer