Question
All is collecting signatures for a petition.
• He currently has 520
signatures.
• He has 6
more weeks to collect the remaining signatures he needs.
• He needs a total of at least 1000
signatures before he can submit the petition.
Ali wants to collect the same number of signatures each week.
Which number line represents all possible numbers of signatures Ali could collect in each of the remaining weeks so that he will have enough signatures to submit the petition?
A
B
C
D
Answers
GPT-4o mini
To determine how many signatures Ali needs to collect each week, let's start with the information provided:
1. Ali's current number of signatures: 520
2. Total signatures needed: 1000
3. Signatures still needed: \( 1000 - 520 = 480 \)
4. Remaining weeks to collect signatures: 6
Now, we need to calculate how many signatures he needs to collect each week to reach his goal. Since he needs 480 more signatures and has 6 weeks to collect them, we can find the number of signatures he needs to collect each week by dividing the total signatures needed by the number of weeks:
\[
\text{Signatures needed per week} = \frac{480}{6} = 80
\]
Thus, Ali needs to collect a minimum of 80 signatures per week. If he collects more than 80 signatures each week, he would also still meet his goal. Therefore, the number of signatures he can collect each week must be at least 80, which leads us to the inequality:
\[
x \geq 80
\]
Where \( x \) is the number of signatures collected each week.
On a number line, this can be represented as a line starting from 80 and extending indefinitely to the right.
- If option A shows a line starting at 80 and extending to the right, then that would be the correct representation of all possible numbers of signatures Ali could collect in each of the remaining weeks so that he will have enough signatures to submit the petition.
Make sure to check each option presented to you to find the one that accurately reflects this situation.
1. Ali's current number of signatures: 520
2. Total signatures needed: 1000
3. Signatures still needed: \( 1000 - 520 = 480 \)
4. Remaining weeks to collect signatures: 6
Now, we need to calculate how many signatures he needs to collect each week to reach his goal. Since he needs 480 more signatures and has 6 weeks to collect them, we can find the number of signatures he needs to collect each week by dividing the total signatures needed by the number of weeks:
\[
\text{Signatures needed per week} = \frac{480}{6} = 80
\]
Thus, Ali needs to collect a minimum of 80 signatures per week. If he collects more than 80 signatures each week, he would also still meet his goal. Therefore, the number of signatures he can collect each week must be at least 80, which leads us to the inequality:
\[
x \geq 80
\]
Where \( x \) is the number of signatures collected each week.
On a number line, this can be represented as a line starting from 80 and extending indefinitely to the right.
- If option A shows a line starting at 80 and extending to the right, then that would be the correct representation of all possible numbers of signatures Ali could collect in each of the remaining weeks so that he will have enough signatures to submit the petition.
Make sure to check each option presented to you to find the one that accurately reflects this situation.