John is 3 years younger than Kiara. At the time when both of them married, the sum of ages of both Kiara and John was 45 years. What was the age of John’s younger brother, Sam, at the time of John’s marriage, if Sam was 5 years younger than John? (in years)

Options

A. 17
B. 15
C. 16
D. 20

Answer

To solve the problem step by step, we will define the ages of John and Kiara at the time of their marriage and then find out the age of John's younger brother, Sam.

### Step 1: Define the ages
Let Kiara's age at the time of marriage be represented as \( X \). Since John is 3 years younger than Kiara, we can express John's age as \( X - 3 \).

**Hint:** Define variables for the ages based on the relationships given in the problem.

### Step 2: Set up the equation
According to the problem, the sum of their ages at the time of marriage is 45 years. Therefore, we can set up the equation:
\[ X + (X - 3) = 45 \]

**Hint:** Use the information about the sum of their ages to create an equation.

### Step 3: Simplify the equation
Now, simplify the equation:
\[ X + X - 3 = 45 \]
This simplifies to:
\[ 2X - 3 = 45 \]

**Hint:** Combine like terms to simplify the equation.

### Step 4: Solve for \( X \)
Next, we will add 3 to both sides of the equation:
\[ 2X = 45 + 3 \]
\[ 2X = 48 \]
Now, divide both sides by 2:
\[ X = \frac{48}{2} = 24 \]

**Hint:** Isolate the variable to find its value.

### Step 5: Find John's age
Now that we have Kiara's age, we can find John's age:
\[ \text{John's age} = X - 3 = 24 - 3 = 21 \]

**Hint:** Use the defined relationship to find John's age.

### Step 6: Find Sam's age
Since Sam is 5 years younger than John, we can find Sam's age:
\[ \text{Sam's age} = \text{John's age} - 5 = 21 - 5 = 16 \]

**Hint:** Again, use the relationship provided in the problem to find Sam's age.

### Conclusion
At the time of John's marriage, Sam was 16 years old.

**Final Answer:** 16 years

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