Question

Michael and Lindsey are saving money.  Michael begins with $20 and saves $5 per week.  Lindsey begins with no money, but saves $10 per week.

Enter the number of weeks it will take for Lindsey and Michael to save the same amount of money.

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 weeks

Michael and Lindsey are saving money.  Michael begins with $20 and saves $5 per week.  Lindsey begins with no money, but saves $10 per week.

Enter the number of weeks it will take for Lindsey and Michael to save the same amount of money.

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ñ

 weeks

Answer 1

To find out when Michael and Lindsey will have the same amount of money, we can set up equations for the amount of money they have after \( w \) weeks.

For Michael:
- He starts with $20 and saves $5 per week.
- The amount of money Michael has after \( w \) weeks can be expressed as:
\[
M(w) = 20 + 5w
\]

For Lindsey:
- She starts with $0 and saves $10 per week.
- The amount of money Lindsey has after \( w \) weeks can be expressed as:
\[
L(w) = 10w
\]

To find when both amounts are equal, we can set the two equations equal to each other:
\[
20 + 5w = 10w
\]

Now, solve for \( w \):
1. Subtract \( 5w \) from both sides:
\[
20 = 10w - 5w
\]
\[
20 = 5w
\]

2. Now divide both sides by 5:
\[
w = \frac{20}{5} = 4
\]

So, it will take **4 weeks** for Lindsey and Michael to save the same amount of money.