If `(x)/(y)=(4)/(3) and (x)/(k)=(1)/(2)`, what is the value of `(k)/(y)`?

Options

A. `(3)/(8)`
B. `(2)/(3)`
C. `(3)/(2)`
D. `(8)/(2)`

Answer

To solve the problem step by step, we will use the given ratios to find the value of \( \frac{k}{y} \).

### Step 1: Write down the given ratios
We have two ratios:
1. \( \frac{x}{y} = \frac{4}{3} \)
2. \( \frac{x}{k} = \frac{1}{2} \)

### Step 2: Express \( k \) in terms of \( x \)
From the second ratio \( \frac{x}{k} = \frac{1}{2} \), we can express \( k \) in terms of \( x \):
\[ k = \frac{2x}{1} = 2x \]

### Step 3: Substitute \( k \) in the expression \( \frac{k}{y} \)
Now we need to find \( \frac{k}{y} \):
\[ \frac{k}{y} = \frac{2x}{y} \]

### Step 4: Substitute \( \frac{x}{y} \) from the first ratio
From the first ratio \( \frac{x}{y} = \frac{4}{3} \), we can substitute \( \frac{x}{y} \) in our expression:
\[ \frac{k}{y} = 2 \cdot \frac{x}{y} = 2 \cdot \frac{4}{3} \]

### Step 5: Calculate the value
Now we calculate:
\[ \frac{k}{y} = 2 \cdot \frac{4}{3} = \frac{8}{3} \]

### Final Answer
Thus, the value of \( \frac{k}{y} \) is \( \frac{8}{3} \).

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