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Molly and Lynn both set aside money weekly for their savings. Molly already has [tex]$\$[/tex]650[tex]$ set aside and adds $[/tex]\[tex]$35$[/tex] each week. Lynn already has [tex]$\$[/tex]825[tex]$ set aside but adds only $[/tex]\[tex]$15$[/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]$650 + 35w \ \textless \ 825 + 15w$[/tex]

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

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

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



Answer :

GinnyAnswer
To determine the number of weeks [tex]\( w \)[/tex] it will take for Molly's savings to exceed Lynn's savings, we need to create an inequality that compares their savings over time.

First, let's understand how each person's savings accumulate:
- Molly starts with \[tex]$650 and adds \$[/tex]35 every week. Therefore, her total savings after [tex]\( w \)[/tex] weeks can be represented by the expression [tex]\( 650 + 35w \)[/tex].
- Lynn starts with \[tex]$825 and adds \$[/tex]15 every week. Therefore, her total savings after [tex]\( w \)[/tex] weeks can be represented by the expression [tex]\( 825 + 15w \)[/tex].

We want to find the point at which Molly's savings exceed Lynn's savings. Therefore, we set up the inequality:

[tex]\[ 650 + 35w > 825 + 15w \][/tex]

This inequality represents the relationship between their savings.

So, the correct answer is:
B. [tex]\( 650 + 35w > 825 + 15w \)[/tex]

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