A certain number is divided into two parts such that 5 times the firsts part added to 11 times the second part makes 7 times the whole. The ratio of the first part to the second part is

Options

A. `1 : 2`
B. `5 : 11`
C. `1 : 2`
D. `2 : 3`

Answer

To solve the problem, we need to define the two parts of the number. Let's denote the first part as \( x \) and the second part as \( y \).

### Step 1: Set up the equation based on the problem statement.
According to the problem, we have:
\[ 5x + 11y = 7(x + y) \]

### Step 2: Expand the equation.
Now, we will expand the right side of the equation:
\[ 5x + 11y = 7x + 7y \]

### Step 3: Rearrange the equation.
Next, we will rearrange the equation to isolate terms involving \( x \) and \( y \):
\[ 5x + 11y - 7x - 7y = 0 \]
This simplifies to:
\[ -2x + 4y = 0 \]

### Step 4: Simplify the equation.
We can simplify this equation further:
\[ 2y = x \]
or
\[ \frac{x}{y} = 2 \]

### Step 5: Find the ratio of the first part to the second part.
The ratio of the first part \( x \) to the second part \( y \) is:
\[ \frac{x}{y} = 2:1 \]

### Final Answer:
The ratio of the first part to the second part is \( 2:1 \).

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