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


A$650 + 35w > 825 + 15w$
B$650w + 35 < 825w + 15$
C$650w + 35 > 825w + 15$
D$650 + 35w < 825 + 15w$

Verified Answer :

  • Represent Molly's savings as \(650 + 35w\).
  • Represent Lynn's savings as \(825 + 15w\).
  • Express the condition that Molly's savings exceed Lynn's as \(650 + 35w > 825 + 15w\).
  • The correct inequality is \(\boxed{650 + 35w > 825 + 15w}\).

Explanation

  1. Formulating the Inequality

To determine the number of weeks \(w\) it will take for Molly's savings to exceed Lynn's savings, we first define the total savings for each person after \(w\) weeks.

Molly starts with \(\$650\) and adds \(\$35\) each week. Therefore, her total savings after \(w\) weeks can be represented as:
\[S_M = 650 + 35w\]

Lynn starts with \(\$825\) and adds \(\$15\) each week. Therefore, her total savings after \(w\) weeks can be represented as:
\[S_L = 825 + 15w\]

We want to find when Molly's savings are greater than Lynn's savings, which corresponds to the inequality:
\[S_M > S_L\]

Substituting the expressions for \(S_M\) and \(S_L\), we get:
\[650 + 35w > 825 + 15w\]
This inequality allows us to determine the number of weeks \(w\) for which Molly's savings will exceed Lynn's savings. Comparing this with the provided options, we can see that it matches the first choice.

Examples

This scenario illustrates how linear inequalities help compare two growing financial plans. By setting up equations based on starting balances and constant rates of change, we can determine the time threshold required for one plan to overtake another. This technique is widely used in financial planning, such as comparing investment growth rates or savings strategies over time.

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