Math worksheet featuring input-output tables and addition problems for practice.

Problem Analysis and Solution

The image contains two main sections:
1. Filling in the blanks and writing rules for input-output relationships (Questions 47, 48, and 49).
2. Matching answers with questions involving addition (Question 50).

Let's solve each section step by step.

---

Section 1: Input-Output Relationships

#### Question 47
| Input | Output |
|-------|--------|
| 5 | 20 |
| 9 | 36 |
| 7 | ? |
| 6 | ? |

Step 1: Identify the pattern.
- For Input = 5, Output = 20.
- For Input = 9, Output = 36.
- Notice that the output is the square of the input:
\[
5^2 = 25 \quad \text{(but given as 20, so there might be an offset or error)}.
\]
\[
9^2 = 81 \quad \text{(but given as 36, so there might be an offset or error)}.
\]

Upon closer inspection, it seems the outputs are not perfect squares but rather multiples of the inputs. Let's recheck:
- \( 5 \times 4 = 20 \)
- \( 9 \times 4 = 36 \)

So, the rule appears to be: Output = Input × 4.

Step 2: Apply the rule to fill in the blanks.
- For Input = 7:
\[
Output = 7 \times 4 = 28
\]
- For Input = 6:
\[
Output = 6 \times 4 = 24
\]

Final Answer for Question 47:
| Input | Output |
|-------|--------|
| 5 | 20 |
| 9 | 36 |
| 7 | 28 |
| 6 | 24 |

Rule: \( Output = Input \times 4 \).

---

#### Question 48
| Input | Output |
|-------|--------|
| 2 | 6 |
| 8 | 24 |
| 1 | ? |
| 9 | ? |

Step 1: Identify the pattern.
- For Input = 2, Output = 6.
- For Input = 8, Output = 24.
- Notice that the output is three times the input:
\[
2 \times 3 = 6
\]
\[
8 \times 3 = 24
\]

So, the rule appears to be: Output = Input × 3.

Step 2: Apply the rule to fill in the blanks.
- For Input = 1:
\[
Output = 1 \times 3 = 3
\]
- For Input = 9:
\[
Output = 9 \times 3 = 27
\]

Final Answer for Question 48:
| Input | Output |
|-------|--------|
| 2 | 6 |
| 8 | 24 |
| 1 | 3 |
| 9 | 27 |

Rule: \( Output = Input \times 3 \).

---

#### Question 49
| Input | Output |
|-------|--------|
| 9 | 27 |
| 4 | 12 |
| 6 | ? |
| 2 | ? |

Step 1: Identify the pattern.
- For Input = 9, Output = 27.
- For Input = 4, Output = 12.
- Notice that the output is three times the input:
\[
9 \times 3 = 27
\]
\[
4 \times 3 = 12
\]

So, the rule appears to be: Output = Input × 3.

Step 2: Apply the rule to fill in the blanks.
- For Input = 6:
\[
Output = 6 \times 3 = 18
\]
- For Input = 2:
\[
Output = 2 \times 3 = 6
\]

Final Answer for Question 49:
| Input | Output |
|-------|--------|
| 9 | 27 |
| 4 | 12 |
| 6 | 18 |
| 2 | 6 |

Rule: \( Output = Input \times 3 \).

---

Section 2: Matching Answers with Questions

#### Question 50
We need to solve each addition problem and match the result with the corresponding letter.

1. a. \( 22 + 14 \)
\[
22 + 14 = 36
\]
Match: \( F = 36 \)

2. b. \( 61 + 13 \)
\[
61 + 13 = 74
\]
Match: \( D = 74 \)

3. c. \( 41 + 1 \)
\[
41 + 1 = 42
\]
Match: \( H = 42 \)

4. d. \( 183 + 16 \)
\[
183 + 16 = 199
\]
Match: \( I = 199 \)

5. e. \( 128 + 2 \)
\[
128 + 2 = 130
\]
Match: \( B = 130 \)

6. f. \( 130 + 14 \)
\[
130 + 14 = 144
\]
Match: \( G = 144 \)

7. g. \( 79 + 14 \)
\[
79 + 14 = 93
\]
Match: \( A = 93 \)

8. h. \( 127 + 11 \)
\[
127 + 11 = 138
\]
Match: \( J = 138 \)

9. i. \( 195 + 4 \)
\[
195 + 4 = 199
\]
Match: \( I = 199 \)

10. j. \( 119 + 19 \)
\[
119 + 19 = 138
\]
Match: \( C = 138 \)

Final Answer for Question 50:
\[
\begin{aligned}
&\text{a. } 22 + 14 = F = 36 \\
&\text{b. } 61 + 13 = D = 74 \\
&\text{c. } 41 + 1 = H = 42 \\
&\text{d. } 183 + 16 = I = 199 \\
&\text{e. } 128 + 2 = B = 130 \\
&\text{f. } 130 + 14 = G = 144 \\
&\text{g. } 79 + 14 = A = 93 \\
&\text{h. } 127 + 11 = J = 138 \\
&\text{i. } 195 + 4 = I = 199 \\
&\text{j. } 119 + 19 = C = 138 \\
\end{aligned}
\]

---

Final Answers

1. Question 47:
\[
\boxed{Output = Input \times 4}
\]
| Input | Output |
|-------|--------|
| 5 | 20 |
| 9 | 36 |
| 7 | 28 |
| 6 | 24 |

2. Question 48:
\[
\boxed{Output = Input \times 3}
\]
| Input | Output |
|-------|--------|
| 2 | 6 |
| 8 | 24 |
| 1 | 3 |
| 9 | 27 |

3. Question 49:
\[
\boxed{Output = Input \times 3}
\]
| Input | Output |
|-------|--------|
| 9 | 27 |
| 4 | 12 |
| 6 | 18 |
| 2 | 6 |

4. Question 50:
\[
\boxed{
\begin{aligned}
&\text{a. } F = 36 \\
&\text{b. } D = 74 \\
&\text{c. } H = 42 \\
&\text{d. } I = 199 \\
&\text{e. } B = 130 \\
&\text{f. } G = 144 \\
&\text{g. } A = 93 \\
&\text{h. } J = 138 \\
&\text{i. } I = 199 \\
&\text{j. } C = 138 \\
\end{aligned}
}
\]