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Molly and Lynn both set aside money weekly for their savings. Molly already has [tex]$\$650$[/tex] set aside and adds [tex]$\[tex]$35$[/tex][/tex] each week. Lynn already has [tex]$\$825$[/tex] set aside but adds only [tex]$\[tex]$15$[/tex][/tex] each week. Which inequality could they use to determine how many weeks, [tex]w[/tex], it will take for Molly's savings to exceed Lynn's savings?

A. [tex]650w + 35 \ \textless \ 825w + 15[/tex]

B. [tex]650w + 35 \ \textgreater \ 825w + 15[/tex]

C. [tex]650 + 35w \ \textgreater \ 825 + 15w[/tex]

D. [tex]650 + 35w \ \textless \ 825 + 15w[/tex]

Sagot :

GinnyAnswer
To determine when Molly's savings will exceed Lynn's savings, we need to set up an inequality that compares the two savings accounts over time.

1. Identify the initial savings and weekly contributions for each:
- Molly:
- Initial savings: \[tex]$650 - Weekly addition: \$[/tex]35
- Lynn:
- Initial savings: \[tex]$825 - Weekly addition: \$[/tex]15

2. Formulate the expression for each person's savings over time [tex]\(w\)[/tex] weeks:
- Molly's savings after [tex]\(w\)[/tex] weeks: [tex]\( 650 + 35w \)[/tex]
- Lynn's savings after [tex]\(w\)[/tex] weeks: [tex]\( 825 + 15w \)[/tex]

3. Set up the inequality to find when Molly's savings exceed Lynn's savings:
- We need the inequality [tex]\( 650 + 35w > 825 + 15w \)[/tex].

4. Interpret the inequality:
- This inequality shows the comparison of Molly’s total savings to Lynn’s total savings over [tex]\(w\)[/tex] weeks.

Therefore, the correct answer is:

C. [tex]\( 650 + 35w > 825 + 15w \)[/tex]
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