Question

All is collecting signatures for a petition.
• He currently has
signatures.
​• He has
more weeks to collect the remaining signatures he needs.
​• He needs a total of at least
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

Answer 1

To determine the number line that represents all possible signatures Ali could collect each week, we need to translate your information into an equation and find the necessary variables.

1. Let's denote:
- \( S \): current number of signatures Ali has
- \( T \): total number of signatures needed
- \( W \): number of weeks left to gather signatures
- \( X \): number of signatures collected each week

2. The total number of signatures Ali will have after \( W \) weeks is:
\[
S + (X \times W)
\]

3. We want this total to be at least \( T \) for Ali to submit his petition:
\[
S + (X \times W) \geq T
\]

4. Rearranging this gives us:
\[
X \times W \geq T - S
\]

\[
X \geq \frac{T - S}{W}
\]

This means that the minimum number of signatures Ali needs to collect each week, \( X \), must be at least \( \frac{T - S}{W} \).

The solution would produce a number line that shows all possible values of \( X \) starting from \( \frac{T - S}{W} \) to any upper limit (possibly extending to positive infinity).

To find the correct number line representation, you would need information on what the values of \( S \), \( T \), and \( W \) actually are, as well as the ranges given on options A, B, C, and D.

If you provide these values and the options available, I can help you determine which number line represents all possible values of \( X \).