Final answer:
Through setting up and solving a system of equations, we find that Imran is 25 years old, Glyn is 16 years old, and Sheila is 8 years old. Their ages were determined by their given relationships and the fact that their ages sum to 49.
Step-by-step explanation:
To solve the problem involving the ages of Imran, Glyn, and Sheila, which is a system of equations problem, we need to write down the equations based on the information given:
- Imran is 9 years older than Glyn: I = G + 9
- Glyn is twice as old as Sheila: G = 2S
- The sum of their ages is 49 years: I + G + S = 49
Next, we can substitute I and G from the first two equations into the third equation to find the age of Sheila:
(G + 9) + G + (G/2) = 49
Multiplying every term by 2 to avoid fractions, we get:
2G + 18 + 2G + G = 98
Combining like terms:
5G + 18 = 98
Subtracting 18 from both sides:
5G = 80
Dividing by 5:
G = 16
Using Glyn's age, we can find Sheila's age (since she is half as old as Glyn):
S = G/2
S = 16/2
S = 8
And lastly, Imran's age can be calculated as:
I = G + 9
I = 16 + 9
I = 25
Thus, Imran is 25 years old, Glyn is 16 years old, and Sheila is 8 years old.