Question

Question
Chanille has a credit card with a $6,000 limit. She charges $750 every month for clothes, but she can only pay back $300 a month. How many months until her card reaches or exceeds its limit?(1 point)
Responses

14 months
14 months
13 months
13 months
8 months
8 months
20 months

Answer 1

To determine how many months it will take for Chanille's credit card balance to reach or exceed the $6,000 limit, we need to calculate her net balance change per month.

1. **Monthly Charges**: $750
2. **Monthly Payments**: $300

**Net Increase in Balance per Month**:
Net increase = Monthly Charges - Monthly Payments
Net increase = $750 - $300 = $450

Now, we will calculate how many months it will take for the balance to reach the limit.

3. **Current Balance**: $0 (initially)
4. **Limit**: $6,000

We need to find the number of months (let's call it \( n \)) required for her balance to exceed $6,000:

\[ \text{Balance after n months} = 450n \]

Set this greater than or equal to $6,000 to find \( n \):

\[ 450n \geq 6,000 \]

Now, divide both sides by 450:

\[ n \geq \frac{6,000}{450} \]
\[ n \geq 13.33 \]

Since \( n \) must be a whole number (representing months), we round up to the nearest month. So, Chanille's balance will reach or exceed $6,000 in 14 months.

Thus, the answer is **14 months**.