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Let's break down the problem and solve it step by step:

1. The total cost for attending the university for the first year is **$19,700**.
2. The student's grandparents will cover **half** of this cost, meaning they will pay:
   \[
   \frac{19,700}{2} = 9,850
   \]
3. An athletic scholarship will pay an additional **$5,000**.

The remaining amount the student needs to pay is:
\[
19,700 - 9,850 - 5,000 = 4,850
\]

4. The student wants to pay this remaining cost over 12 months, so we divide the remaining balance by 12:
\[
\frac{4,850}{12} \approx 404.17
\]

Therefore, the amount the student will need to save every month is closest to **$404.17**, which corresponds to **option A**.

Let me know if you need more details or have any questions!

Here are 5 related questions for further practice:
1. If the athletic scholarship was $1,000 less, how much would the student have to save monthly?
2. What if the grandparents paid only 40% of the total cost? How would the monthly savings change?
3. How much would the student need to save monthly if they wanted to pay off the balance in 18 months instead?
4. If the student could increase their monthly savings by $50, how much time would it take to pay off the $4,850?
5. What percentage of the total cost is covered by the athletic scholarship?

**Tip:** Always break down word problems by identifying what is given, then calculate step by step!

The total cost of attending a state university is $19,700 for the first year. A student's grandparents will pay half of this cost. An athletic scholarship will pay another $5,000. Which amount is closest to the minimum that the student will need to save every month in order to pay off the remaining cost at the end of 12 months?

Find out how to calculate the monthly savings needed to cover the remaining cost of university tuition after contributions from grandparents and an athletic scholarship. The problem involves basic arithmetic operations including subtraction and division, suitable for Grades 6-8.

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