x is greater than y by 12 and the respective ratio, between x and y is 3 :2. What is the sum of a third number z and x if is `1/3` of y ?

Options

A. 40.25
B. 42
C. 43.5
D. 44

Answer

To solve the problem step by step, we will first establish the relationships between the variables \( x \), \( y \), and \( z \) based on the information given in the question.

### Step 1: Set up the equations based on the problem statement.
We know from the problem that:
1. \( x \) is greater than \( y \) by 12, which can be expressed as:
\[ x = y + 12 \]
2. The ratio of \( x \) to \( y \) is \( 3:2 \). This can be expressed mathematically as:
\[ \frac{x}{y} = \frac{3}{2} \]
From this, we can also express \( x \) in terms of \( y \):
\[ x = \frac{3}{2}y \]

### Step 2: Equate the two expressions for \( x \).
Now we have two expressions for \( x \):
1. \( x = y + 12 \)
2. \( x = \frac{3}{2}y \)

Setting them equal to each other:
\[ y + 12 = \frac{3}{2}y \]

### Step 3: Solve for \( y \).
To solve for \( y \), we can rearrange the equation:
\[ 12 = \frac{3}{2}y - y \]
\[ 12 = \frac{3}{2}y - \frac{2}{2}y \]
\[ 12 = \frac{1}{2}y \]
Multiplying both sides by 2:
\[ y = 24 \]

### Step 4: Substitute \( y \) back to find \( x \).
Now that we have \( y \), we can find \( x \):
\[ x = y + 12 = 24 + 12 = 36 \]

### Step 5: Find \( z \).
According to the problem, \( z \) is \( \frac{1}{3} \) of \( y \):
\[ z = \frac{1}{3}y = \frac{1}{3} \times 24 = 8 \]

### Step 6: Calculate the sum of \( x \) and \( z \).
Now we need to find the sum of \( x \) and \( z \):
\[ x + z = 36 + 8 = 44 \]

### Conclusion:
The final answer is:
\[ \text{The sum of } z \text{ and } x \text{ is } 44. \]