Question
Emma buys 256 beads she give away 96 and uses what she has left which graph shows the possible number she can make necklaces with
Answers
GPT-4o mini
To determine how many necklaces Emma can make after buying 256 beads and giving away 96, we first need to calculate how many beads she has left.
1. **Calculate the number of beads left:**
\[
256 \text{ (total beads)} - 96 \text{ (given away)} = 160 \text{ beads left}
\]
2. **Determine the possible number of necklaces she can make:**
The number of necklaces Emma can make will depend on how many beads she uses for each necklace. If we let \( x \) represent the number of beads used per necklace, then the number of necklaces she can make, \( N \), can be calculated as:
\[
N = \frac{160}{x}
\]
3. **Possible values for \( x \):**
Since \( x \) must be a positive integer (she can't use a fraction of a bead), the possible values for \( x \) are any of the divisors of 160. The divisors are:
- 1
- 2
- 4
- 5
- 8
- 10
- 16
- 20
- 32
- 40
- 80
- 160
4. **Create the graph:**
You would generate a graph with \( x \) values on the x-axis (each divisor representing beads per necklace) and \( N \) values on the y-axis, showing how many necklaces can be made for each divisor.
You’d plot points such as:
- For \( x = 1 \), \( N = 160 \)
- For \( x = 2 \), \( N = 80 \)
- For \( x = 4 \), \( N = 40 \)
- For \( x = 5 \), \( N = 32 \)
- For \( x = 8 \), \( N = 20 \)
- For \( x = 10 \), \( N = 16 \)
- For \( x = 16 \), \( N = 10 \)
- For \( x = 20 \), \( N = 8 \)
- For \( x = 32 \), \( N = 5 \)
- For \( x = 40 \), \( N = 4 \)
- For \( x = 80 \), \( N = 2 \)
- For \( x = 160 \), \( N = 1 \)
5. **Conclusion:**
Look for a graph that shows \( N \) decreasing as \( x \) increases. The exact shape of the graph will depend on the values you plot, but you can expect downward descending points. Any graph with this structure would represent the possible number of necklaces Emma can make based on the number of beads she uses for each necklace.
1. **Calculate the number of beads left:**
\[
256 \text{ (total beads)} - 96 \text{ (given away)} = 160 \text{ beads left}
\]
2. **Determine the possible number of necklaces she can make:**
The number of necklaces Emma can make will depend on how many beads she uses for each necklace. If we let \( x \) represent the number of beads used per necklace, then the number of necklaces she can make, \( N \), can be calculated as:
\[
N = \frac{160}{x}
\]
3. **Possible values for \( x \):**
Since \( x \) must be a positive integer (she can't use a fraction of a bead), the possible values for \( x \) are any of the divisors of 160. The divisors are:
- 1
- 2
- 4
- 5
- 8
- 10
- 16
- 20
- 32
- 40
- 80
- 160
4. **Create the graph:**
You would generate a graph with \( x \) values on the x-axis (each divisor representing beads per necklace) and \( N \) values on the y-axis, showing how many necklaces can be made for each divisor.
You’d plot points such as:
- For \( x = 1 \), \( N = 160 \)
- For \( x = 2 \), \( N = 80 \)
- For \( x = 4 \), \( N = 40 \)
- For \( x = 5 \), \( N = 32 \)
- For \( x = 8 \), \( N = 20 \)
- For \( x = 10 \), \( N = 16 \)
- For \( x = 16 \), \( N = 10 \)
- For \( x = 20 \), \( N = 8 \)
- For \( x = 32 \), \( N = 5 \)
- For \( x = 40 \), \( N = 4 \)
- For \( x = 80 \), \( N = 2 \)
- For \( x = 160 \), \( N = 1 \)
5. **Conclusion:**
Look for a graph that shows \( N \) decreasing as \( x \) increases. The exact shape of the graph will depend on the values you plot, but you can expect downward descending points. Any graph with this structure would represent the possible number of necklaces Emma can make based on the number of beads she uses for each necklace.