Final answer:
By setting up algebraic equations based on the problem statements and solving them, we determined that Mr. Henderson is 72 years old and his granddaughter is 8 years old now. The provided options in the question do not include the correct answer, indicating a possible error in the options.
Step-by-step explanation:
The student is dealing with an algebra problem involving simultaneous equations. We can represent the current age of Mr. Henderson as H and his granddaughter's age as G. Initially, we are told that Mr. Henderson is nine times as old as his granddaughter: H = 9G. In 8 years, Mr. Henderson's age will be H + 8, and his granddaughter's age will be G + 8. At that time, he will be five times older than her: H + 8 = 5(G + 8). To find their current ages, we solve these two equations.
- Substitute the first equation into the second: 9G + 8 = 5G + 40.
- Solve for G: 4G = 32, so G = 8.
- Use G's value to find H: H = 9 × 8 = 72.
Therefore, Mr. Henderson is 72 years old and his granddaughter is 8 years old now which does not match any of the provided options a), b), c), or d). There might be a mistake in the options provided as none of them is the correct solution to the algebraic equations derived from the problem statements.