To determine the number of weeks [tex]\( w \)[/tex] it will take for Molly's savings to exceed Lynn's savings, we need to compare their respective savings amounts.
1. Molly's savings starts with \[tex]$650 and increases by \$[/tex]35 each week. Her total savings after [tex]\( w \)[/tex] weeks can be expressed as:
[tex]\[
650 + 35w
\][/tex]
2. Lynn's savings starts with \[tex]$825 and increases by \$[/tex]15 each week. Her total savings after [tex]\( w \)[/tex] weeks can be expressed as:
[tex]\[
825 + 15w
\][/tex]
We want to find the inequality that determines when Molly's savings will be greater than Lynn's savings. Therefore, we need the inequality:
[tex]\[
650 + 35w > 825 + 15w
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{650 + 35w > 825 + 15w}
\][/tex]
This corresponds to answer option D.
