QUESTION
The product of the ages of Adu and Tanko is 9 less than Akorfa's age. If Tanko is 4 years older than Adu and Akorfa's age is six times Tanko's age, find Akorfa's age.
SOLUTION
Let Adu's age be $x$ years.
Tanko is 4 years older than Adu, so Tanko's age is:
$$
x + 4
$$
Akorfa's age is six times Tanko's age, therefore:
$$
6(x + 4)
$$
According to the question:
> The product of the ages of Adu and Tanko is 9 less than Akorfa's age.
So we form the equation:
$$
x(x + 4) = 6(x + 4) - 9
$$
Expand both sides:
$$
x^2 + 4x = 6x + 24 - 9
$$
Simplify:
$$
x^2 + 4x = 6x + 15
$$
Bring all terms to one side:
$$
x^2 + 4x - 6x - 15 = 0
$$
$$
x^2 - 2x - 15 = 0
$$
Factorize:
$$
(x - 5)(x + 3) = 0
$$
Solve for $x$:
$$
x - 5 = 0
$$
or
$$
x + 3 = 0
$$
Therefore,
$$
x = 5
$$
or
$$
x = -3
$$
Since age cannot be negative:
$$
x = 5
$$
So, Adu's age is:
$$
5 \text{ years}
$$
Tanko's age is:
$$
5 + 4 = 9 \text{ years}
$$
Akorfa's age is:
$$
6 \times 9 = 54 \text{ years}
$$
Therefore, Akorfa's age is:
$$
\boxed{54 \text{ years}}
$$
