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Let's solve each of these questions step by step.

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### Question 14:
**Problem Statement:**
A wizard named Nepo says: "I am only three times my son's age. My father is 40 years more than twice my age. Together the three of us are a mere 1240 years old." How old is Nepo?

**Solution:**
Let's define:
- \( S \) = Son's age
- \( N \) = Nepo's age
- \( F \) = Father's age

Given:
1. Nepo’s age is three times his son's age:
   \[
   N = 3S
   \]

2. Nepo's father is 40 years more than twice Nepo's age:
   \[
   F = 2N + 40
   \]

3. The sum of their ages is 1240:
   \[
   S + N + F = 1240
   \]

#### Step 1: Substitute \( N = 3S \) into the other equations
Using \( N = 3S \) in equation 3:
\[
S + 3S + F = 1240
\]
\[
4S + F = 1240
\]

#### Step 2: Substitute \( F = 2N + 40 \) into the equation
Since \( N = 3S \), then \( F = 2(3S) + 40 \):
\[
F = 6S + 40
\]

Substitute \( F = 6S + 40 \) into the equation \( 4S + F = 1240 \):
\[
4S + 6S + 40 = 1240
\]
\[
10S + 40 = 1240
\]
\[
10S = 1200
\]
\[
S = 120
\]

#### Step 3: Find Nepo's age \( N \) and his father’s age \( F \)
1. \( N = 3S = 3 \times 120 = 360 \)
2. \( F = 6S + 40 = 6 \times 120 + 40 = 720 \)

**Answer:** Nepo's age is **360 years**.

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### Question 15:
**Problem Statement:**
A is as much younger than B as he is older than C. If the sum of the ages of B and C is 50 years, what is definitely the difference between ages of A and B?

**Solution:**
Let:
- \( A \) = Age of A
- \( B \) = Age of B
- \( C \) = Age of C

Given:
1. A is as much younger than B as he is older than C.
   This implies that:
   \[
   B - A = A - C
   \]

2. The sum of ages of B and C is 50:
   \[
   B + C = 50
   \]

#### Step 1: Solve the age difference equation
Rearrange \( B - A = A - C \):
\[
B + C = 2A
\]

#### Step 2: Substitute \( B + C = 50 \)
Since \( B + C = 50 \), we have:
\[
2A = 50
\]
\[
A = 25
\]

#### Step 3: Substitute \( A = 25 \) back to find \( B - A \)
Since \( B - A = A - C \) and \( B + C = 50 \):
- \( B - A = 25 - C \)
- The difference

Learn how to solve age-related algebra problems involving equations and substitutions. The solutions explain how to determine Nepo's age and the difference between ages of A and B, suitable for students in Grades 8-10.

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