X is four years older than Y who is twice as old as Z. If the total ages of X, Y and Z be 34, how old is X?

Options

A. (a) 8
B. (b) 10
C. (c) 12
D. (d) 16

Explanation

To solve the problem step by step, let's denote the ages of X, Y, and Z as follows:

1. Let the age of Z be \( z \).
2. Since Y is twice as old as Z, we can express Y's age as:
\[ Y = 2z \]
3. X is 4 years older than Y, so we can express X's age as:
\[ X = Y + 4 = 2z + 4 \]
4. According to the problem, the total ages of X, Y, and Z is 34:
\[ X + Y + Z = 34 \]
Substituting the expressions for X and Y into this equation gives:
\[ (2z + 4) + (2z) + z = 34 \]
5. Now, combine the terms:
\[ 2z + 4 + 2z + z = 34 \]
This simplifies to:
\[ 5z + 4 = 34 \]
6. Next, subtract 4 from both sides to isolate the term with z:
\[ 5z = 30 \]
7. Now, divide by 5 to solve for z:
\[ z = 6 \]
8. Now that we have Z's age, we can find Y's age:
\[ Y = 2z = 2 \times 6 = 12 \]
9. Finally, we can find X's age:
\[ X = Y + 4 = 12 + 4 = 16 \]

Thus, the age of X is **16 years**.