Question
Kelly has $250 n her piggy bank and is making $25 per day she referees. Melissa has $320 in per piggy bank and is making $15 per day doing chores. How long will it take for Kelly to have more money than Melissa?
Question 14 options:
More than 3 days
More than 7 days
More than 5 days
More than 2 days
Question 14 options:
More than 3 days
More than 7 days
More than 5 days
More than 2 days
Answers
GPT-4o mini
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.**
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.**