If 50% of a certain number is equal to `3/4th` of another number, what is the ratio between the numbers?

Options

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

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Understand the Problem
We are given that 50% of a certain number (let's call it \( x \)) is equal to \( \frac{3}{4} \) of another number (let's call it \( y \)). We need to find the ratio between these two numbers \( x \) and \( y \).

### Step 2: Set Up the Equation
From the problem, we can write the equation:
\[ 50\% \text{ of } x = \frac{3}{4} \text{ of } y \]
This can be expressed mathematically as:
\[ \frac{50}{100} \cdot x = \frac{3}{4} \cdot y \]

### Step 3: Simplify the Equation
We can simplify \( \frac{50}{100} \) to \( \frac{1}{2} \):
\[ \frac{1}{2} \cdot x = \frac{3}{4} \cdot y \]

### Step 4: Rearrange the Equation
To find the ratio \( \frac{x}{y} \), we can rearrange the equation:
\[ x = \frac{3}{4} \cdot y \cdot 2 \]
This simplifies to:
\[ x = \frac{3}{2} \cdot y \]

### Step 5: Find the Ratio
Now, we can express the ratio \( \frac{x}{y} \):
\[ \frac{x}{y} = \frac{3}{2} \]
Thus, the ratio of \( x \) to \( y \) is:
\[ x : y = 3 : 2 \]

### Conclusion
The ratio between the two numbers \( x \) and \( y \) is \( 3 : 2 \).

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