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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

1 answer

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.