If `(c-3d)/(4)=(d)/(2)`, what is the ratio of c to d?

Options

A. `5:1`
B. `3:2`
C. `4:3`
D. `3:4`

Answer

To solve the equation \(\frac{c - 3d}{4} = \frac{d}{2}\) and find the ratio of \(c\) to \(d\), follow these steps:

### Step 1: Eliminate the fractions
Multiply both sides of the equation by 4 to eliminate the denominator:

\[ c - 3d = 4 \cdot \frac{d}{2} \]

### Step 2: Simplify the right side
Calculate \(4 \cdot \frac{d}{2}\):

\[ c - 3d = 2d \]

### Step 3: Isolate \(c\)
Add \(3d\) to both sides to isolate \(c\):

\[ c = 2d + 3d \]

### Step 4: Combine like terms
Combine the terms on the right side:

\[ c = 5d \]

### Step 5: Find the ratio of \(c\) to \(d\)
To find the ratio of \(c\) to \(d\), divide both sides by \(d\):

\[ \frac{c}{d} = \frac{5d}{d} \]

### Step 6: Simplify the ratio
This simplifies to:

\[ \frac{c}{d} = 5 \]

Thus, the ratio of \(c\) to \(d\) is:

\[ c : d = 5 : 1 \]

### Final Answer
The ratio of \(c\) to \(d\) is \(5:1\).

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