To determine how many weeks, [tex]\( w \)[/tex], it will take for Molly's savings to exceed Lynn's savings, we need to compare their total savings over time.
First, let's write expressions for Molly's total savings and Lynn's total savings after [tex]\( w \)[/tex] weeks:
1. Molly's initial savings are \[tex]$650, and she adds \$[/tex]35 each week. Therefore, her total savings after [tex]\( w \)[/tex] weeks is:
[tex]\[
\text{Molly's Total Savings} = 650 + 35w
\][/tex]
2. Lynn's initial savings are \[tex]$825, and she adds \$[/tex]15 each week. Therefore, her total savings after [tex]\( w \)[/tex] weeks is:
[tex]\[
\text{Lynn's Total Savings} = 825 + 15w
\][/tex]
We want to find the condition where Molly's total savings exceed Lynn's total savings. Therefore, we set up the following inequality:
[tex]\[
650 + 35w > 825 + 15w
\][/tex]
This inequality shows the condition where Molly's total savings will be greater than Lynn's total savings after [tex]\( w \)[/tex] weeks.
The correct answer is:
[tex]\[
\boxed{D. \ 650 + 35w > 825 + 15w}
\][/tex]
