Find the value of x if 5:3 :: x: 6.

Answer

To solve the problem, we need to find the value of \( x \) in the proportion \( 5:3 :: x:6 \). Here’s the step-by-step solution:

### Step 1: Set up the proportion
We start with the given ratio:
\[ 5:3 = x:6 \]
This means that the two ratios are equal. We can express this as a fraction:
\[ \frac{5}{3} = \frac{x}{6} \]

### Step 2: Cross-multiply
To solve for \( x \), we will use cross-multiplication. This means we will multiply the numerator of one fraction by the denominator of the other fraction:
\[ 5 \times 6 = 3 \times x \]
This simplifies to:
\[ 30 = 3x \]

### Step 3: Solve for \( x \)
Now, we need to isolate \( x \). We can do this by dividing both sides of the equation by 3:
\[ x = \frac{30}{3} \]
Calculating this gives:
\[ x = 10 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{10} \]

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