To determine the inequality that shows how many weeks [tex]\( w \)[/tex] it will take for Molly's savings to exceed Lynn's savings, let's analyze the situation step-by-step:
1. Identify the initial savings and weekly additions:
- Molly starts with \[tex]$650 and adds \$[/tex]35 each week.
- Lynn starts with \[tex]$825 and adds \$[/tex]15 each week.
2. Write the expressions for their savings after [tex]\( w \)[/tex] weeks:
- Molly’s savings after [tex]\( w \)[/tex] weeks will be [tex]\( 650 + 35w \)[/tex].
- Lynn’s savings after [tex]\( w \)[/tex] weeks will be [tex]\( 825 + 15w \)[/tex].
3. Set up the inequality to find the point where Molly's savings exceed Lynn's savings:
- We want to find the number of weeks, [tex]\( w \)[/tex], when [tex]\( 650 + 35w \)[/tex] becomes greater than [tex]\( 825 + 15w \)[/tex].
4. Formulate the inequality:
- The inequality can be written as:
[tex]\[
650 + 35w > 825 + 15w
\][/tex]
5. Choose the correct option:
- Option A: [tex]\( 650w + 35 < 825w + 15 \)[/tex]
- This is not correct because it misplaces the w associated with the constant terms.
- Option B: [tex]\(650 + 35w > 825 + 15w\)[/tex]
- This is correct as it accurately captures the expressions for the savings and the inequality indicating when Molly’s savings exceed Lynn’s.
- Option C: [tex]\( 650 + 35w < 825 + 15w \)[/tex]
- This is incorrect because it shows when Molly’s savings are lesser, not greater.
- Option D: [tex]\( 650w + 35 > 825w + 15 \)[/tex]
- This is incorrect because it misplaces the w associated with the constant terms.
Thus, the correct inequality to determine how many weeks it will take for Molly's savings to exceed Lynn's savings is:
Answer: B. [tex]\( 650 + 35w > 825 + 15w \)[/tex]
