The image presents the following question:

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.

Solution:

(a) Forming an equation:

• Fiona's age = $x$ years
• Thomas's age = $x + 3$ years (since he is 3 years older than Fiona)
• Cara's age = $2x$ years (since she is twice as old as Fiona)

The sum of their ages is given as 51, so the equation becomes: $x + (x + 3) + 2x = 51$

Simplify the equation: $x + x + 3 + 2x = 51$ $4x + 3 = 51$

(b) Solving the equation:

Now, solve for $x$: $4x = 51 - 3$ $4x = 48$ $x = \frac{48}{4} = 12$

So, Fiona is 12 years old.

• Thomas is $x + 3 = 12 + 3 = 15$ years old.
• Cara is $2x = 2(12) = 24$ years old.

Final Ages:

• Fiona: 12 years
• Thomas: 15 years
• Cara: 24 years

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. If the sum of their ages was 60 instead of 51, what would their ages be?
2. How would the equation change if Thomas was 5 years older than Fiona instead of 3?
3. What if Cara was three times as old as Fiona—how would that affect their ages?
4. If Fiona’s age was halved, how would the total change?
5. Can you set up and solve a similar equation where their total age is 75?

Tip: When forming equations, always express every variable in terms of a single unknown to simplify solving.