Solve for `x : (x)/(5) + (x)/(7) = 12`

Options

A. 70
B. 140
C. 35
D. 105

Explanation

To solve the equation \(\frac{x}{5} + \frac{x}{7} = 12\), we will follow these steps:

### Step 1: Find a common denominator
The denominators in the fractions are 5 and 7. The least common multiple (LCM) of 5 and 7 is 35.

### Step 2: Rewrite the fractions with the common denominator
We will rewrite each fraction with 35 as the denominator:
\[ \frac{x}{5} = \frac{7x}{35} \quad \text{(since } 5 \times 7 = 35\text{)} \]
\[ \frac{x}{7} = \frac{5x}{35} \quad \text{(since } 7 \times 5 = 35\text{)} \]

### Step 3: Combine the fractions
Now we can add the two fractions:
\[ \frac{7x}{35} + \frac{5x}{35} = \frac{7x + 5x}{35} = \frac{12x}{35} \]

### Step 4: Set the equation equal to 12
Now we have:
\[ \frac{12x}{35} = 12 \]

### Step 5: Eliminate the fraction by multiplying both sides by 35
To eliminate the fraction, multiply both sides by 35:
\[ 12x = 12 \times 35 \]

### Step 6: Calculate the right side
Now calculate \(12 \times 35\):
\[ 12 \times 35 = 420 \]
So, we have:
\[ 12x = 420 \]

### Step 7: Solve for \(x\)
Now divide both sides by 12 to solve for \(x\):
\[ x = \frac{420}{12} \]

### Step 8: Simplify the fraction
Now simplify \(\frac{420}{12}\):
\[ x = 35 \]

### Final Answer
Thus, the solution for \(x\) is:
\[ \boxed{35} \]

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