Question 15

Explanation

Let $B$ be Bimo's current age and $A$ be his Father's current age. We will translate the verbal information from the problem into a precise mathematical model.

First, let's analyze the past condition: "Six years ago, Bimo's age was $4$ years younger than one-sixth of his Father's age." This sentence can be written as the following equation:

Second, let's analyze the current condition: "Bimo's current age is $3$ years older than one-eighth of his Father's age." This statement yields the second equation:

Now we have a system of linear equations with two variables. The next step is to simplify the first equation to make it easier to work with. We will eliminate the fractions and group the variables:

Next, we modify the second equation to have a form consistent with equation $(1)$ to facilitate the elimination process:

With two neat linear equations, we can eliminate variable $A$ by subtracting equation $(1)$ from equation $(2)$:

Having found that Bimo is $9$ years old, we substitute the value of $B$ into equation $(1)$ to find the Father's age:

Finally, we calculate the sum of Bimo's and his Father's current ages:

Thus, the sum of their ages is 57 years.