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The image you uploaded contains a problem related to estimating the amount of study expenses to be funded by means other than scholarships. Here's the transcription of the problem:

**Problem:**
A university student is trying to estimate the amount of study that needs to be funded by other means than scholarships. From his family’s experience, the amount is about 5 times the amount he could fund with scholarships on average. If the student estimates that he will need about 18,000 euros for a year for his living expenses and tuition:

a) What is the amount that he needs to fund by other means than scholarships (given that he is well-motivated and capable to study)?  
Form a system of equations and solve.

b) If the amount covered by scholarships grows by 2/3, how much is the share of other funding as a percentage?

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### Solution:

Let's define the variables:
- Let \( S \) be the amount he could fund with scholarships.
- Let \( O \) be the amount he needs to fund by other means.

From the problem, we have the following information:
1. \( O = 5S \) (The amount to be funded by other means is 5 times the amount covered by scholarships)
2. \( S + O = 18,000 \) (Total expenses including both scholarships and other means is 18,000 euros)

#### (a) Form a system of equations and solve:

The system of equations is:
\[
\begin{cases}
O = 5S \\
S + O = 18,000
\end{cases}
\]

Substitute \( O = 5S \) into the second equation:
\[
S + 5S = 18,000
\]
\[
6S = 18,000
\]
\[
S = \frac{18,000}{6} = 3,000
\]

Now, substituting \( S = 3,000 \) back into the first equation:
\[
O = 5(3,000) = 15,000
\]

So, the student needs to fund 15,000 euros by other means.

#### (b) If the amount covered by scholarships grows by 2/3, how much is the share of other funding as a percentage?

If the scholarship amount increases by \( \frac{2}{3} \), the new scholarship amount \( S' \) will be:
\[
S' = S + \frac{2}{3}S = \frac{5}{3}S
\]
Substitute the value of \( S = 3,000 \):
\[
S' = \frac{5}{3} \times 3,000 = 5,000
\]

Now, the remaining amount \( O' \) that needs to be funded by other means will be:
\[
O' = 18,000 - 5,000 = 13,000
\]

Finally, the share of other funding as a percentage is:
\[
\text{Percentage of other funding} = \left(\frac{O'}{18,000}\right) \times 100 = \left(\frac{13,000}{18,000}\right) \times 100 \approx 72.22\%
\]

### Summary:
- **(a)** The student needs to fund 15,000 euros by other means.
- **(b)** After the scholarship increases, the share of other funding is approximately 72.22%.

Would you like more details or have any questions?

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### Related Questions:
1. What if the initial funding from scholarships was only half of what was estimated?
2. How would the problem change if the total required amount increased to 20,000 euros?
3. What would the new percentage be if the scholarship only increased by 50% instead of 2/3?
4. How would the amount to be funded by other means change if the student managed to reduce the total expenses by 10%?
5. What if the scholarship amount doubled instead of increasing by 2/3?

### Tip:
Always double-check the relationship between variables in word problems to ensure the system of equations is set up correctly. This will help avoid calculation errors.

A university student is trying to estimate the amount of study that needs to be funded by other means than scholarships. From his family’s experience, the amount is about 5 times the amount he could fund with scholarships on average. If the student estimates that he will need about 18,000 euros for a year for his living expenses and tuition:

a) What is the amount that he needs to fund by other means than scholarships (given that he is well-motivated and capable to study)?

b) If the amount covered by scholarships grows by 2/3, how much is the share of other funding as a percentage?

Solve a real-world problem involving estimating study expenses by setting up a system of linear equations. This problem covers algebraic concepts such as solving for variables and calculating percentages, suitable for students in Grades 9-12.

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