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 1,000 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?
• He currently has 520 signatures.
• He has 6 more weeks to collect the remaining signatures he needs.
• He needs a total of at least 1,000 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?
Answers
GPT-4o mini
To find the number of signatures Ali needs to collect each week, let's start by determining how many additional signatures he needs.
1. **Total signatures needed**: 1,000
2. **Current signatures collected**: 520
3. **Signatures still needed**:
\[
1000 - 520 = 480
\]
Ali has 6 weeks to collect the 480 signatures. To find out how many signatures he needs to collect each week, we can divide the total number of signatures he still needs by the number of weeks:
\[
\text{Signatures per week} = \frac{480}{6} = 80
\]
Thus, Ali needs to collect at least 80 signatures each week to reach his goal.
To express this mathematically, let \( x \) represent the number of signatures Ali collects each week. Then we have the inequality:
\[
6x \geq 480
\]
By solving this inequality, we divide both sides by 6:
\[
x \geq 80
\]
This means that the number of signatures Ali could collect each week must be at least 80.
On the number line, you would represent all values \( x \) where \( x \) is greater than or equal to 80. This is typically represented with a closed circle at 80 (indicating that he can collect 80 signatures or more) and a line extending to the right side (indicating all numbers greater than 80).
So, the number line would look like this:
- A closed dot at 80
- A line extending to the right of 80, indicating \( x \geq 80 \)
This visualization conveys that Ali can collect any number of signatures starting from 80 upwards.
1. **Total signatures needed**: 1,000
2. **Current signatures collected**: 520
3. **Signatures still needed**:
\[
1000 - 520 = 480
\]
Ali has 6 weeks to collect the 480 signatures. To find out how many signatures he needs to collect each week, we can divide the total number of signatures he still needs by the number of weeks:
\[
\text{Signatures per week} = \frac{480}{6} = 80
\]
Thus, Ali needs to collect at least 80 signatures each week to reach his goal.
To express this mathematically, let \( x \) represent the number of signatures Ali collects each week. Then we have the inequality:
\[
6x \geq 480
\]
By solving this inequality, we divide both sides by 6:
\[
x \geq 80
\]
This means that the number of signatures Ali could collect each week must be at least 80.
On the number line, you would represent all values \( x \) where \( x \) is greater than or equal to 80. This is typically represented with a closed circle at 80 (indicating that he can collect 80 signatures or more) and a line extending to the right side (indicating all numbers greater than 80).
So, the number line would look like this:
- A closed dot at 80
- A line extending to the right of 80, indicating \( x \geq 80 \)
This visualization conveys that Ali can collect any number of signatures starting from 80 upwards.