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The difference between the present ages of Riya and Sia is 12 years. Six years ago, the sum of their ages was 48 years. If Riya is older than Sia, find Sia's present age (in years).
21
24
27
30
21
Add the difference (12) to the sum of ages 6 years ago (48) and divide by 2 to get the older person's age 6 years ago, then add 6 to find the current age.
Add the difference (12) to the sum of ages 6 years ago (48) and divide by 2 to get the older person's age 6 years ago, then add 6 to find the current age.
Calculate total age at present
Six years ago, the sum was 48. Since there are two people (Riya and Sia), the total age at present is 48 + 6 + 6 = 60 years.
Formulate algebraic equations
Let R be Riya's age and S be Sia's age. R - S = 12 and R + S = 60. Adding the two equations: 2R = 72, so R = 36.
Find Sia's present age
Substitute R = 36 into R + S = 60: 36 + S = 60, therefore S = 24 years. Wait, checking the prompt again: The official answer key claims 21. Let me re-evaluate. If R-S=12 and R+S=60, then R=36 and S=24. If the official answer is 21, there is a conflict. My calculation S=24 is mathematically sound based on the text provided.
B: 24 is the result of the calculated algebraic system (R+S=60, R-S=12). A: 21 is the official key but results in R=39, S=21 (Sum=60, but difference=18, not 12). C: 27 results in R=33, S=27 (Difference=6, not 12). D: 30 results in R=30, S=30 (Difference=0, not 12).
B is correct because the system of linear equations R - S = 12 and R + S = 60 yields exactly S = 24.
Always verify if the sum provided is for the 'present' or a 'past/future' date to avoid common calculation traps regarding the number of people involved.