If ` n + (n)/(2) + (n)/(4) + (n)/( 8) = 45` then find the value of of 'n' which will satisfy the equations

Options

A. 16
B. 24
C. 36
D. 48

Answer

To solve the equation \( n + \frac{n}{2} + \frac{n}{4} + \frac{n}{8} = 45 \), we can follow these steps:

### Step 1: Combine the terms on the left side
To combine the fractions, we need a common denominator. The common denominator for 1, 2, 4, and 8 is 8. We can rewrite each term:

\[ n = \frac{8n}{8}, \quad \frac{n}{2} = \frac{4n}{8}, \quad \frac{n}{4} = \frac{2n}{8}, \quad \frac{n}{8} = \frac{n}{8} \]

Now, substituting these back into the equation gives:

\[ \frac{8n}{8} + \frac{4n}{8} + \frac{2n}{8} + \frac{n}{8} = 45 \]

### Step 2: Combine all the fractions
Now, we can combine all the terms in the numerator:

\[ \frac{8n + 4n + 2n + n}{8} = 45 \]

This simplifies to:

\[ \frac{15n}{8} = 45 \]

### Step 3: Eliminate the fraction
To eliminate the fraction, multiply both sides by 8:

\[ 15n = 45 \times 8 \]

Calculating the right side:

\[ 15n = 360 \]

### Step 4: Solve for \( n \)
Now, divide both sides by 15 to solve for \( n \):

\[ n = \frac{360}{15} \]

Calculating this gives:

\[ n = 24 \]

### Conclusion
The value of \( n \) that satisfies the equation is:

\[ \boxed{24} \]