To solve the problem, we need to identify the pattern or rule governing the given equations. Let's analyze the provided examples step by step:
Given Equations:
1. \( 21 + 10 = 31 \)
2. \( 22 + 20 = 84 \)
3. \( 23 + 30 = 159 \)
We are tasked with finding the result of \( 24 + 50 \).
---
Step 1: Analyze the Pattern
Let's break down each equation to see if there is a consistent rule.
#### Equation 1: \( 21 + 10 = 31 \)
- Here, \( 21 + 10 \) simply adds up to \( 31 \). This looks like a straightforward addition.
#### Equation 2: \( 22 + 20 = 84 \)
- If we add \( 22 + 20 \), we get \( 42 \), but the result is \( 84 \). This suggests that there might be a multiplication involved.
#### Equation 3: \( 23 + 30 = 159 \)
- If we add \( 23 + 30 \), we get \( 53 \), but the result is \( 159 \). Again, this suggests a multiplication pattern.
---
Step 2: Hypothesize a Rule
From the above observations, it appears that the results are not just simple additions. Instead, there might be a combination of addition and multiplication. Let's hypothesize a rule of the form:
\[
\text{Result} = (a + b) \times c
\]
where \( a \) and \( b \) are the numbers being "added," and \( c \) is some factor that depends on the numbers.
#### Test the Hypothesis:
1. For \( 21 + 10 = 31 \):
- \( 21 + 10 = 31 \)
- Here, \( c = 1 \) because \( (21 + 10) \times 1 = 31 \).
2. For \( 22 + 20 = 84 \):
- \( 22 + 20 = 42 \)
- The result is \( 84 \), which is \( 42 \times 2 \).
- Here, \( c = 2 \).
3. For \( 23 + 30 = 159 \):
- \( 23 + 30 = 53 \)
- The result is \( 159 \), which is \( 53 \times 3 \).
- Here, \( c = 3 \).
---
Step 3: Identify the Pattern for \( c \)
From the above examples:
- For \( 21 + 10 \), \( c = 1 \).
- For \( 22 + 20 \), \( c = 2 \).
- For \( 23 + 30 \), \( c = 3 \).
It appears that \( c \) increases by 1 for each subsequent equation. Therefore, for the next equation (\( 24 + 50 \)), we expect \( c = 4 \).
---
Step 4: Apply the Rule to \( 24 + 50 \)
Using the rule:
\[
\text{Result} = (a + b) \times c
\]
where:
- \( a = 24 \)
- \( b = 50 \)
- \( c = 4 \)
Calculate:
\[
a + b = 24 + 50 = 74
\]
\[
\text{Result} = 74 \times 4 = 296
\]
---
Final Answer:
\[
\boxed{296}
\]
Parent Tip: Review the logic above to help your child master the concept of riddle math.
