To determine how many months it will take for Chanille's credit card balance to reach or exceed the $6,000 limit, we can calculate the net effect of her charges and payments each month.
- Monthly charge: $750
- Monthly payment: $300
- Net increase in debt per month: $750 - $300 = $450
Now, we need to find out how many months it will take for her balance to reach or exceed $6,000.
Since the credit card starts at $0, we can set up the equation for the total debt after \( m \) months as follows:
\[ \text{Total debt} = 450m \]
We want to find \( m \) when the total debt reaches $6,000:
\[ 450m \geq 6000 \]
Now, solving for \( m \):
\[ m \geq \frac{6000}{450} \approx 13.33 \]
Since \( m \) must be a whole number, we round up to the next whole number, which is 14.
Thus, it will take Chanille 14 months for her credit card to reach or exceed its limit.
The correct response is 14 months.