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.
(b) Solve the equation and work out Michael's and Jenny's ages.

Question 7: Fiona is x years old.
Thomas is 3 years older than Fiona.
Cara is twice as old as Fiona.
The sum of their ages is 51.
(a) Form an equation in terms of x.
(b) Solve the equation and work out Fiona's, Thomas's and Cara's ages.

Question 8: Alan is x years old.
Barry is ten years younger than Alan.
Kevin is double Alan's age.
The sum of their ages is 54.
(a) Form an equation in terms of x.
(b) Solve the equation and work out Alan's, Barry's and Kevin's ages.

Question 6: Form the equation x + 2 x = 57 , solve for x to find Michael's age, then calculate Jenny's age. Michael is 19 ​ years old and Jenny is 38 ​ years old.
Question 7: Form the equation x + ( x + 3 ) + 2 x = 51 , solve for x to find Fiona's age, then calculate Thomas's and Cara's ages. Fiona is 12 ​ years old, Thomas is 15 ​ years old, and Cara is 24 ​ years old.
Question 8: Form the equation x + ( x − 10 ) + 2 x = 54 , solve for x to find Alan's age, then calculate Barry's and Kevin's ages. Alan is 16 ​ years old, Barry is 6 ​ years old, and Kevin is 32 ​ years old.

Explanation

Problem Analysis Let's break down each question step by step to form equations and solve for the ages of the individuals involved. We'll tackle questions 6, 7, and 8 sequentially.

Solving Question 6 Question 6:


(a) Forming the equation: Michael's age is represented by x . Jenny's age is twice Michael's age, so Jenny is 2 x years old. The sum of their ages is 57. Therefore, the equation is: x + 2 x = 57
(b) Solving the equation: Combine like terms: 3 x = 57 Divide both sides by 3: x = 3 57 ​ = 19 So, Michael is 19 years old. Jenny is 2 x = 2 × 19 = 38 years old.

Solving Question 7 Question 7:

(a) Forming the equation: Fiona's age is x . Thomas is 3 years older than Fiona, so Thomas is x + 3 years old. Cara is twice as old as Fiona, so Cara is 2 x years old. The sum of their ages is 51. Therefore, the equation is: x + ( x + 3 ) + 2 x = 51
(b) Solving the equation: Combine like terms: 4 x + 3 = 51 Subtract 3 from both sides: 4 x = 51 − 3 = 48 Divide both sides by 4: x = 4 48 ​ = 12 So, Fiona is 12 years old. Thomas is x + 3 = 12 + 3 = 15 years old. Cara is 2 x = 2 × 12 = 24 years old.

Solving Question 8 Question 8:

(a) Forming the equation: Alan's age is x . Barry is ten years younger than Alan, so Barry is x − 10 years old. Kevin is double Alan's age, so Kevin is 2 x years old. The sum of their ages is 54. Therefore, the equation is: x + ( x − 10 ) + 2 x = 54
(b) Solving the equation: Combine like terms: 4 x − 10 = 54 Add 10 to both sides: 4 x = 54 + 10 = 64 Divide both sides by 4: x = 4 64 ​ = 16 So, Alan is 16 years old. Barry is x − 10 = 16 − 10 = 6 years old. Kevin is 2 x = 2 × 16 = 32 years old.

Final Answers In summary:


Question 6: Michael is 19 years old, and Jenny is 38 years old.
Question 7: Fiona is 12 years old, Thomas is 15 years old, and Cara is 24 years old.
Question 8: Alan is 16 years old, Barry is 6 years old, and Kevin is 32 years old.

Examples
Understanding how to set up and solve algebraic equations based on age relationships is a fundamental skill that can be applied in various real-life scenarios. For instance, if you're planning a family event and need to determine the ages of different family members to organize appropriate activities, you can use similar equations. Also, in historical contexts, if you know certain age relationships and a total age from a census, you can deduce individual ages using these algebraic techniques. This skill is also useful in puzzles and logical reasoning problems where age relationships are provided to solve for unknown ages.

Answered by GinnyAnswer | 2025-07-05

Michael is 19 years old and Jenny is 38 years old; Fiona is 12 years old, Thomas is 15 years old, and Cara is 24 years old; Alan is 16 years old, Barry is 6 years old, and Kevin is 32 years old.
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Answered by Anonymous | 2025-07-14