Joan's age is 42 years and Kelvin's age is 26 years. How many years ago was Kelvin's age half of Joan's age ?

Options

A. 6 years
B. 4 years
C. 10 years
D. 8 years

Explanation

To solve the problem of how many years ago Kelvin's age was half of Joan's age, we can follow these steps:

### Step 1: Define the current ages
- Joan's current age = 42 years
- Kelvin's current age = 26 years

### Step 2: Define the variable for years ago
Let \( x \) be the number of years ago when Kelvin's age was half of Joan's age.

### Step 3: Write the equations for their ages \( x \) years ago
- Kelvin's age \( x \) years ago = \( 26 - x \)
- Joan's age \( x \) years ago = \( 42 - x \)

### Step 4: Set up the equation based on the condition
According to the problem, Kelvin's age was half of Joan's age \( x \) years ago. Therefore, we can set up the equation:
\[ 26 - x = \frac{1}{2}(42 - x) \]

### Step 5: Solve the equation
To eliminate the fraction, multiply both sides by 2:
\[ 2(26 - x) = 42 - x \]
This simplifies to:
\[ 52 - 2x = 42 - x \]

### Step 6: Rearrange the equation
Now, let's rearrange the equation to isolate \( x \):
\[ 52 - 42 = 2x - x \]
\[ 10 = x \]

### Step 7: Conclusion
Thus, \( x = 10 \). This means that 10 years ago, Kelvin's age was half of Joan's age.

### Verification
To verify:
- 10 years ago, Joan's age = \( 42 - 10 = 32 \)
- 10 years ago, Kelvin's age = \( 26 - 10 = 16 \)

Since \( 16 \) is indeed half of \( 32 \), our solution is confirmed.

### Final Answer
Kelvin's age was half of Joan's age 10 years ago.

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