A university student is trying to estimate the amount of study funds he needs to fund by loan. From his friend's experience, the amount he needs to fund by other means than part-time work is about 5/9 of the amount of the part time work. If the student estimates that he will need about 16 400 euros for a year for his living expenses and tuition, what is the amount he could make monthly by working based on this estimation?



Let the total amount the student needs for living expenses and tuition be denoted by \( 16,400 \) euros for the year. Let the monthly earnings from part-time work be denoted by \( x \).

According to the information given, the student needs to fund about \( \frac{5}{9} \) of his expenses through other means (like loans). The remaining \( \frac{4}{9} \) would then be the portion covered by his part-time work. Therefore, the amount covered by part-time work is \( \frac{4}{9} \) of the total expenses, while the amount covered by loans is \( \frac{5}{9} \).

### Step-by-step solution:

1. The amount covered by part-time work is:
   \[
   \frac{4}{9} \times 16,400 = 7,288.89 \, \text{euros}.
   \]
   
2. Since this is the annual amount earned from part-time work, the monthly earnings would be:
   \[
   \frac{7,288.89}{12} \approx 607.41 \, \text{euros per month}.
   \]

Thus, based on this estimation, the student could make approximately **607.41 euros per month** from part-time work.

Would you like further details or have any questions?

Here are five related questions to expand on this:
1. How much would the student need to borrow annually if part-time work covers a certain amount?
2. What happens if the student can only work fewer hours, reducing their part-time income?
3. What are the effects of interest on a student loan over multiple years?
4. How could living in a city with a higher cost of living impact these estimations?
5. How does working more hours during holidays affect overall income?

**Tip**: Always set aside a buffer in your budget for unexpected expenses such as medical costs or study materials!

A university student is trying to estimate the amount of study funds he needs to fund by loan. From his friend's experience, the amount he needs to fund by other means than part-time work is about 5/9 of the amount of the part time work. If the student estimates that he will need about 16 400 euros for a year for his living expenses and tuition, what is the amount he could make monthly by working based on this estimation?

Learn how to estimate monthly earnings from part-time work based on the total annual living expenses and tuition of 16,400 euros. This problem involves concepts like ratios, proportions, and basic arithmetic calculations. Suitable for high school students in Grades 10-12.

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