To determine the correct inequality that describes when Molly's savings will exceed Lynn's savings, we need to start by writing expressions for each person's savings after [tex]\(w\)[/tex] weeks.
1. Molly's Savings:
- Initial savings: \[tex]$650
- Weekly addition: \$[/tex]35
- Total savings after [tex]\(w\)[/tex] weeks: [tex]\(650 + 35w\)[/tex]
2. Lynn's Savings:
- Initial savings: \[tex]$825
- Weekly addition: \$[/tex]15
- Total savings after [tex]\(w\)[/tex] weeks: [tex]\(825 + 15w\)[/tex]
We seek the point at which Molly's savings will be greater than Lynn's savings, represented mathematically by:
[tex]\[
650 + 35w > 825 + 15w
\][/tex]
Now let's inspect the provided answer choices:
A. [tex]\(650 + 35w > 825 + 15w\)[/tex]
B. [tex]\(650 + 95w < 825 + 15w\)[/tex]
C. [tex]\(650w + 35 > 825w + 15\)[/tex]
D. [tex]\(650w + 35 < 825w + 15\)[/tex]
Looking at the options above, it's clear that the inequality marking the point where Molly’s savings exceed Lynn's (i.e., option A) correctly represents our derived inequality:
[tex]\[
650 + 35w > 825 + 15w
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{A. \, 650+35w>825+15w}
\][/tex]
