The average age of Donald his wife and their two children is 23 years. His wife is just 4 years younger than Donald himself and his Wife was 24 years old when his daughter was born. He was 32 years old when his son was born. The average age of Donald and his daughter is :

Options

A. 25 years
B. 22.5 years
C. 26 years
D. Can't determined

Answer

To solve the problem step by step, let's break down the information provided and find the average age of Donald and his daughter.

### Step 1: Calculate the total age of the family
The average age of Donald, his wife, and their two children is 23 years. Since there are 4 people in the family, we can calculate the total age of the family.

**Total Age = Average Age × Number of People**
Total Age = 23 years × 4 = 92 years

**Hint:** Remember that the average is calculated by dividing the total by the number of items.

### Step 2: Establish the relationship between Donald and his wife
We know that Donald's wife is 4 years younger than Donald. Let's denote Donald's age as D and his wife's age as W.

**W = D - 4**

**Hint:** When dealing with age differences, always express one person's age in terms of another.

### Step 3: Determine the ages based on children’s birth
The problem states that Donald's wife was 24 years old when their daughter was born. This means that the age difference between Donald's wife and their daughter is 24 years.

Let’s denote the daughter’s age as A. Therefore, when the daughter was born, the wife was 24 years old, and Donald would have been:

**D = W + 4 = 24 + 4 = 28 years old** (when daughter was born)

**Hint:** Use the ages at the time of birth to establish current ages.

### Step 4: Calculate current ages based on the son’s birth
The problem also states that Donald was 32 years old when his son was born. Let’s denote the son’s age as B. This means that:

**B = D - 32**
**B = 28 - 32 = -4** (This indicates that the son is currently younger than the daughter)

Since we know the total age of the family is 92 years, we can express the ages of the children in terms of the ages of the parents.

### Step 5: Set up the equations
Now, we have:
- Total age = D + W + A + B = 92
- W = D - 4
- A = W - 24
- B = D - 32

Substituting W into the total age equation:
- D + (D - 4) + (W - 24) + (D - 32) = 92

### Step 6: Solve for Donald's age
Substituting W:
- D + (D - 4) + (D - 28) + (D - 32) = 92
- 4D - 64 = 92
- 4D = 156
- D = 39 years

### Step 7: Calculate the wife’s age
Now that we have Donald's age, we can find his wife's age:
- W = D - 4 = 39 - 4 = 35 years

### Step 8: Calculate the children’s ages
Now we can find the ages of the children:
- A (daughter's age) = W - 24 = 35 - 24 = 11 years
- B (son's age) = D - 32 = 39 - 32 = 7 years

### Step 9: Find the average age of Donald and his daughter
Now we can find the average age of Donald and his daughter:
- Average age = (D + A) / 2 = (39 + 11) / 2 = 50 / 2 = 25 years

### Final Answer:
The average age of Donald and his daughter is **25 years**.