If `(1)/(5)x+(1)/(7)y=3`, what is the value of `7x+5y`?

Answer

To solve the equation \(\frac{1}{5}x + \frac{1}{7}y = 3\) and find the value of \(7x + 5y\), we will follow these steps:

### Step 1: Write the given equation
We start with the equation:
\[ \frac{1}{5}x + \frac{1}{7}y = 3 \]

### Step 2: Find the least common multiple (LCM)
To eliminate the fractions, we need to find the least common multiple of the denominators, which are 5 and 7. The LCM of 5 and 7 is 35.

### Step 3: Multiply the entire equation by the LCM
Now, we multiply the entire equation by 35 to eliminate the fractions:
\[ 35 \left(\frac{1}{5}x\right) + 35 \left(\frac{1}{7}y\right) = 35 \cdot 3 \]

### Step 4: Simplify the equation
This simplifies to:
\[ 7x + 5y = 105 \]

### Step 5: Identify the value of \(7x + 5y\)
From the simplified equation, we can see that:
\[ 7x + 5y = 105 \]

Thus, the value of \(7x + 5y\) is **105**.

### Summary
The final answer is:
\[ \boxed{105} \]

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