Final answer:
To find the present ages of A and B, two equations were created from the given conditions. After solving the simultaneous equations, it was found that A is 25 years old and B is 10 years old, corresponding to answer option c.
Step-by-step explanation:
The student's question revolves around finding the present ages of two individuals, A and B, given conditions about their ages in the past and future. To solve this problem, we will establish two equations based on the descriptions provided.
Let's denote A's current age as A, and B's current age as B. Five years ago, A's age was 4 times B's age, which gives us the first equation:
Equation 1: A - 5 = 4(B - 5)
In 5 years, A's age will be twice that of B. This gives us the second equation:
Equation 2: A + 5 = 2(B + 5)
To find the solution, we need to solve these two equations simultaneously. Let's simplify them:
- Equation 1 leads to A = 4B - 15
- Equation 2 leads to A = 2B + 5
As we have two equations with the same A, we can set them equal to each other:
4B - 15 = 2B + 5
After solving, we get B = 10. Plugging this value into either equation gives A = 25. Therefore, the present ages of A and B are 25 years and 10 years, respectively, which corresponds to option c.