If `8 : x :: 16 : 35`, find the value of x.

Answer

To solve the proportion \( 8 : x :: 16 : 35 \), we can set up the equation using the property of proportions. This means we can write:

\[ \frac{8}{x} = \frac{16}{35} \]

### Step 1: Cross-multiply the fractions
Cross-multiplying gives us:

\[ 8 \cdot 35 = 16 \cdot x \]

### Step 2: Calculate \( 8 \cdot 35 \)
Now we calculate \( 8 \cdot 35 \):

\[ 8 \cdot 35 = 280 \]

So we have:

\[ 280 = 16 \cdot x \]

### Step 3: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 16:

\[ x = \frac{280}{16} \]

### Step 4: Simplify \( \frac{280}{16} \)
Now we simplify \( \frac{280}{16} \):

\[ x = \frac{280 \div 16}{16 \div 16} = \frac{17.5}{1} = 17.5 \]

Thus, the value of \( x \) is:

\[ \boxed{17.5} \]