The Common Core makes simple math more complicated. Heres why. - Vox - Free Printable

To solve the problem, let's analyze the given pattern step by step and determine the rule governing the operations.

Given Equations:

1. \( 12 + \boxed{3} = 15 \)
2. \( 15 + \boxed{5} = 20 \)
3. \( 20 + \boxed{10} = 30 \)
4. \( 30 + \boxed{2} = 32 \)

We need to find the value of the boxed number in the last equation and then determine the "answer" based on the pattern.

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Step 1: Analyze the Pattern

Let's examine how the boxed numbers are related to the other numbers in each equation.

#### Equation 1:
\[ 12 + \boxed{3} = 15 \]
- The boxed number is \( 3 \).
- Notice that \( 15 - 12 = 3 \).

#### Equation 2:
\[ 15 + \boxed{5} = 20 \]
- The boxed number is \( 5 \).
- Notice that \( 20 - 15 = 5 \).

#### Equation 3:
\[ 20 + \boxed{10} = 30 \]
- The boxed number is \( 10 \).
- Notice that \( 30 - 20 = 10 \).

#### Equation 4:
\[ 30 + \boxed{2} = 32 \]
- The boxed number is \( 2 \).
- Notice that \( 32 - 30 = 2 \).

From these observations, we see that the boxed number in each equation is simply the difference between the result on the right-hand side and the first number on the left-hand side.

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Step 2: Apply the Pattern to Find the Missing Boxed Number

The pattern suggests that the boxed number is the difference between the result and the first number. Let's verify this for the last equation:

\[ 30 + \boxed{?} = 32 \]
- The boxed number is \( 32 - 30 = 2 \).

This matches the given boxed number in the last equation, confirming our pattern.

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Step 3: Determine the "Answer"

The problem asks us to find the value of \( 20 = \text{answer} \). From the pattern, we see that the boxed numbers are derived from the differences. However, the question seems to be asking for a specific value associated with \( 20 \).

Given the sequence of boxed numbers:
- \( 3 \)
- \( 5 \)
- \( 10 \)
- \( 2 \)

We notice that the boxed numbers do not follow a simple arithmetic or geometric progression. Instead, the problem might be asking for the boxed number corresponding to \( 20 \) in a similar setup.

Since the boxed number for \( 30 \) is \( 2 \), and there is no additional context provided for \( 20 \), we can infer that the "answer" is the boxed number associated with \( 20 \) in a similar operation.

Thus, the boxed number for \( 20 \) is \( 10 \) (from the third equation).

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Final Answer:

\[
\boxed{10}
\]