20 : 11 : : 102 : ?radio_button_unchecked49radio_button_unchecked52radio_button_unchecked61radio_button_unchecked98

1. Break Down the Problem

We are given a proportion: $20 : 11 :: 102 : ?$. This means we need to find a value $x$ such that the ratio of $20$ to $11$ is equal to the ratio of $102$ to $x$.

2. Relevant Concepts

The concept of proportionality is used here. If $a : b = c : d$, then $ad = bc$.

3. Analysis and Detail

Using the values from the proportion: $20 : 11 = 102 : x$ can be transformed into the equation: $20 \cdot x = 102 \cdot 11$

Calculating the right-hand side: $102 \cdot 11 = 1122$ Now, substituting back into the equation: $20x = 1122$

4. Verify and Summarize

To find $x$, we solve for $x$: $x = \frac{1122}{20} = 56.1$

However, in the context of the multiple-choice options provided, none of these options reflect this exact calculation.

Final Answer

The options provided do not match the calculated result of $x = 56.1$. Based on the given options $49, 52, 61, 98$, the closest approximate is 52.