Final answer:
To solve this problem, set up a system of equations and solve for x. However, the given information leads to a negative age for A, which is not possible. There may be an error or inconsistency in the question. The correct option is D. 18 years
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's assume the current age of A is 3x and the current age of B is 8x. Six years later, the age of A will be 3x+6 and the age of B will be 8x+6. According to the given information, the ratio of their ages 6 years later is 4:9. So, we have the equation (3x+6)/(8x+6) = 4/9.
Cross-multiplying, we get 36x+54 = 32x+24. Simplifying, we have 4x = -30. Solving for x, we find that x = -7.5. However, since we cannot have a negative age, we discard this solution. Therefore, A's current age is 3x = 3(-7.5) = -22.5 years.
As this is not a possible answer for a person's age, it seems there may be an error or inconsistency in the given information. Please check the question again or consult with your teacher for clarification.
The question involves finding the current age of person A when given a ratio of the ages of A and B currently and another ratio of their ages after six years. This is a problem of ratios and proportions, which is a common topic in middle school mathematics.
Let's denote the current age of A as 3x and the current age of B as 8x since their ages are in the ratio 3:8. Six years later, their ages will become (3x + 6) and (8x + 6), respectively. At this future time, their ages are in the ratio 4:9. To find the current age of A, we can set up the following proportion:
(3x + 6)/(8x + 6) = 4/9
After solving the proportion, we find that x equals 6. So, the current age of A is 3x, which is 3*6 = 18 years.
The correct option is D. 18 years