Judy has $100 and Eleanor has $75. Judy is saving $5 per day and Eleanor is saving $7 per day.

Question

What equation represents how much money Judy will have in total after saving for d days?
What equation represents how much money Eleanor will have in total after saving for d days?
What equation would be used to find out how many days it will take for Judy and Eleanor to have the same amount of money saved?
After the number of days it took both to have the same amount of money saved, how much money do they each have?

Answer 1

Let's break down the problem step by step.

1. Equation for Judy's total money after \( d \) days: Judy starts with $100 and saves $5 per day. Therefore, the equation is: \[ J(d) = 100 + 5d \]

2. Equation for Eleanor's total money after \( d \) days: Eleanor starts with $75 and saves $7 per day. Thus, her equation is: \[ E(d) = 75 + 7d \]

3. Equation to find out how many days it will take for Judy and Eleanor to have the same amount of money saved: To find when their total amounts are equal, set the two equations equal to each other: \[ 100 + 5d = 75 + 7d \]

   To solve for \( d \), rearrange the equation: \[ 100 - 75 = 7d - 5d \] \[ 25 = 2d \] \[ d = \frac{25}{2} = 12.5 \]

4. Calculating how much money they each have after 12.5 days: Plug \( d = 12.5 \) into each equation:

   For Judy: \[ J(12.5) = 100 + 5(12.5) = 100 + 62.5 = 162.5 \]

   For Eleanor: \[ E(12.5) = 75 + 7(12.5) = 75 + 87.5 = 162.5 \]

After 12.5 days, both Judy and Eleanor will each have $162.50.