Seven-ninths of my current age is the same as five-sixths of that of one of my cousins . Thirty-nine years ago my age was twice his age . My current age is ____ years .

Options

A. 60
B. 55
C. 45
D. 50

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information provided.

### Step 1: Define the Variables
Let:
- \( X \) = my current age
- \( Y \) = my cousin's current age

### Step 2: Set Up the First Equation
According to the problem, seven-ninths of my current age is equal to five-sixths of my cousin's age. This can be expressed as:
\[ \frac{7}{9}X = \frac{5}{6}Y \]

### Step 3: Cross-Multiply to Eliminate Fractions
To eliminate the fractions, we can cross-multiply:
\[ 7 \cdot 6X = 5 \cdot 9Y \]
This simplifies to:
\[ 42X = 45Y \]
From this, we can express \( Y \) in terms of \( X \):
\[ Y = \frac{42}{45}X = \frac{14}{15}X \]

### Step 4: Set Up the Second Equation
The problem states that thirty-nine years ago, my age was twice my cousin's age. This can be expressed as:
\[ X - 39 = 2(Y - 39) \]

### Step 5: Expand and Rearrange the Second Equation
Expanding the second equation gives:
\[ X - 39 = 2Y - 78 \]
Rearranging this, we get:
\[ X - 2Y = -39 + 78 \]
\[ X - 2Y = 39 \]

### Step 6: Substitute \( Y \) in the Second Equation
Now, substitute \( Y = \frac{14}{15}X \) into the second equation:
\[ X - 2\left(\frac{14}{15}X\right) = 39 \]
This simplifies to:
\[ X - \frac{28}{15}X = 39 \]

### Step 7: Combine Like Terms
Combining the terms on the left:
\[ \frac{15}{15}X - \frac{28}{15}X = 39 \]
\[ -\frac{13}{15}X = 39 \]

### Step 8: Solve for \( X \)
To find \( X \), multiply both sides by -15/13:
\[ X = 39 \cdot -\frac{15}{13} \]
Calculating this:
\[ X = -\frac{585}{13} = 45 \]

### Conclusion
Thus, my current age is:
\[ \boxed{45} \text{ years} \]