To determine how long it will take for Kelly to have more money than Melissa, we need to formulate the total amount of money each will have over time and find when Kelly's amount exceeds Melissa's.
Let's define:
- \( K \): Kelly's initial amount = $250
- \( M \): Melissa's initial amount = $320
- \( d \): number of days
The amount of money Kelly has after \( d \) days is: \[ K_d = 250 + 25d \]
The amount of money Melissa has after \( d \) days is: \[ M_d = 320 + 15d \]
We want to find when Kelly has more money than Melissa: \[ K_d > M_d \] \[ 250 + 25d > 320 + 15d \]
Subtract \( 15d \) from both sides: \[ 250 + 10d > 320 \]
Next, subtract 250 from both sides: \[ 10d > 70 \]
Now, divide by 10: \[ d > 7 \]
Thus, Kelly will have more money than Melissa in more than 7 days.
The correct choice is: More than 7 days.
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