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

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

B. [tex]$650 m + 35 \ \textless \ 825 m + 15$[/tex]

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

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

Sagot :

GinnyAnsweridn
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.
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