To determine which inequality Molly and Lynn could use to figure out 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. Write down the formula for Molly's savings:
- Molly starts with \[tex]$650 and adds \$[/tex]35 each week.
- Therefore, her savings after [tex]\( w \)[/tex] weeks can be written as:
[tex]\[
650 + 35w
\][/tex]
2. Write down the formula for Lynn's savings:
- Lynn starts with \[tex]$825 and adds \$[/tex]15 each week.
- Therefore, her savings after [tex]\( w \)[/tex] weeks can be written as:
[tex]\[
825 + 15w
\][/tex]
3. Set up the inequality to find when Molly's savings will be greater than Lynn's savings:
- We want to determine the point at which Molly's savings exceed Lynn's savings.
- So, we need to find when:
[tex]\[
650 + 35w > 825 + 15w
\][/tex]
4. Identify the correct inequality from the given options:
- Option A: [tex]\( 650w + 35 < 825w + 15 \)[/tex]
This inequality is not set up correctly because the coefficients and terms are incorrectly placed.
- Option B: [tex]\( 650w + 35 > 825w + 15 \)[/tex]
This inequality is similar to Option A and is incorrectly set up.
- Option C: [tex]\( 650 + 35w > 825 + 15w \)[/tex]
This option correctly represents the relationship we established.
- Option D: [tex]\( 650 + 35w < 825 + 15w \)[/tex]
This option represents the scenario where Molly's savings are less than Lynn's savings, which is not what we are trying to determine.
So, the correct inequality they could use to determine how many weeks, [tex]\( W \)[/tex], it will take for Molly's savings to exceed Lynn's savings is:
[tex]\[
\boxed{650 + 35w > 825 + 15w}
\][/tex]
Therefore, the correct answer is:
C. [tex]\( 650 + 35w > 825 + 15w \)[/tex]
