Question

Kareem is three times as old as his son. After 10 years, the sum of their ages will be 76 years. Find their present ages.

Answer 1

Hint: In this question, we need to determine the present age of Kareem and his son such that the sum of their ages after ten years is 76 years. For this, we will establish the relations between the ages of the Kareem and his son and solve them simultaneously for their present age.

Complete step-by-step answer:
Let the present age of Kareem’s son be ‘x’.
According to the question, the present age of Kareem is three times as old as his son.
So, the present age of Kareem will be ‘3x’.
The age of Kareem’s son after 10 years will be ‘x+10’ years.
Also, the age of Kareem after 10 years will be given as ‘3x+10’ years.
The sum of the ages of the Kareem’s son and Kareem is given as 76 years. Mathematically, $ {A_{K + 10}} + {A_{S + 10}} = 76 $
Substituting the value of the age of Kareem and his son in the equation $ {A_K} + {A_S} = 76 $ to determine the present age of Kareem and his son.
 $
\Rightarrow {A_{K + 10}} + {A_{S + 10}} = 76 \\
\Rightarrow 3x + 10 + x + 10 = 76 \\
\Rightarrow 4x + 20 = 76 \\
\Rightarrow 4x = 56 \\
  x = 14 \\
 $
Hence, the present age of Kareem’s son is 14 years.
Substituting the value of ‘x’ in the function ‘3x’ as the age of the Kareem.
So, Kareem’s age is given as $ 3x = 3 \times 14 = 42 $ years.
Hence, the present age of Kareem and his son is given as 42 years and 14 years respectively.

Note: Students should be very careful while establishing the relationship between the parameters involved in the question. The total number of equations should be equals to the total number of parameters to evaluate all the parameters efficiently.