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Let's go through the questions from the images one by one and solve them:

### Question 4:
**Gregory is \( x \) years old. Daisy is 2 years older than Gregory. The sum of their ages is 40.**

- (a) **Form an equation in terms of \( x \):**
  
  Gregory's age = \( x \)  
  Daisy's age = \( x + 2 \)

  The sum of their ages is given as 40, so:
  \[
  x + (x + 2) = 40
  \]

- (b) **Solve the equation:**
  Simplifying the equation:
  \[
  2x + 2 = 40
  \]
  Subtract 2 from both sides:
  \[
  2x = 38
  \]
  Divide by 2:
  \[
  x = 19
  \]

  So, Gregory is 19 years old, and Daisy, being 2 years older, is:
  \[
  19 + 2 = 21 \text{ years old.}
  \]

---

### Question 5:
**Robert is \( x \) years old. Hannah is 7 years younger than Robert. The sum of their ages is 61.**

- (a) **Form an equation in terms of \( x \):**
  
  Robert's age = \( x \)  
  Hannah's age = \( x - 7 \)

  The sum of their ages is 61, so:
  \[
  x + (x - 7) = 61
  \]

- (b) **Solve the equation:**
  Simplifying the equation:
  \[
  2x - 7 = 61
  \]
  Add 7 to both sides:
  \[
  2x = 68
  \]
  Divide by 2:
  \[
  x = 34
  \]

  So, Robert is 34 years old, and Hannah, being 7 years younger, is:
  \[
  34 - 7 = 27 \text{ years old.}
  \]

---

### Question 6:
**Michael is \( x \) years old. Jenny is twice as old as Michael. The sum of their ages is 57.**

- (a) **Form an equation in terms of \( x \):**
  
  Michael's age = \( x \)  
  Jenny's age = \( 2x \)

  The sum of their ages is 57, so:
  \[
  x + 2x = 57
  \]

- (b) **Solve the equation:**
  Simplifying the equation:
  \[
  3x = 57
  \]
  Divide by 3:
  \[
  x = 19
  \]

  So, Michael is 19 years old, and Jenny, being twice as old, is:
  \[
  2 \times 19 = 38 \text{ years old.}
  \]

---

Would you like to proceed with the next questions or have any specific clarifications? Here are five related questions that can further deepen your understanding:

1. What if Daisy was 5 years older than Gregory? How would the equation change?
2. Can you solve for Robert and Hannah's ages if the sum was instead 70?
3. What if Jenny was three times as old as Michael? How would you set up the equation?
4. How would the equation change if Gregory and Daisy's sum of ages was 50 instead of 40?
5. Can you generalize a formula for two people's ages if one is \( y \) years older than the other and the sum of their ages is \( S \)?

**Tip:** When forming equations for age problems, it's helpful to always express all ages in terms of one variable and then use the information provided (like sum or difference of ages) to set up the equation.

Solve the age-related algebraic equations based on the relationships given in the word problems.

Learn how to solve algebraic word problems involving ages. This exercise covers key algebraic concepts, including setting up linear equations based on word problems. Suitable for students in Grades 6-8.

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