Final answer:
By setting up an algebraic equation based on the given age relationships and sum of ages, we find that Priya is 15 years old, Amirah is 19 years old, and Shirley is 13 years old.
Step-by-step explanation:
Let's denote Priya's age with 'P'. According to the problem, Amirah is 4 years older than Priya, so Amirah's age would be 'P + 4'. Shirley is 2 years younger than Priya, which means Shirley's age is 'P - 2'.
The sum of their ages is 47, so we can write the equation: P + (P + 4) + (P - 2) = 47. Simplifying this, we get 3P + 2 = 47. Subtracting 2 from both sides gives us 3P = 45. Finally, dividing by 3, we find P = 15.
Since we've found Priya's age to be 15, we can now determine Amirah's age by adding 4, which makes it 19. To find out Shirley's age, we subtract 2 from Priya's age, getting 13.
Their ages are:
Priya: 15 years old
Amirah: 19 years old
Shirley: 13 years old
Overall, by setting up and solving a simple algebraic equation, we've determined the respective ages of Amirah, Priya, and Shirley.