Question

The sum of weights of a father and son is 85kg. The weight of the son is $\dfrac{1}{4}$. of the weight of the father. Find their weight?

Answer 1

Hint: At first let us assume the weight of the father and son to be A kg and B kg. It’s given that the sum of the weights to be 85, which gives us A + B = 85, and the weight of the son is $\dfrac{1}{4}$ of the weight of the father which gives us $B = \dfrac{1}{4}A$. By using the method of substitution we can find the value of A and B.

Complete step by step answer:

Let the weight of the father be A kg
And let the weight of the son be B kg
We are given that the sum of the weight of the father and son is 85 kg
$ \Rightarrow A + B = 85$ …………….(1)
We are also given that the weight of the son is $\dfrac{1}{4}$ of the weight of the father.
$ \Rightarrow B = \dfrac{1}{4}A$……………..(2)
Now lets substitute the value of B from (2) in equation (1)
$ \Rightarrow A + \dfrac{1}{4}A = 85$
Taking LCM we get
$\begin{gathered}
   \Rightarrow \dfrac{{4A + A}}{4} = 85 \\
   \Rightarrow 4A + A = 340 \\
   \Rightarrow 5A = 340 \\
   \Rightarrow A = \dfrac{{340}}{5} = 68 \\
\end{gathered} $
From this we get that weight of the father is 68 kg
Now substitute the value of A in equation (2)
$\begin{gathered}
   \Rightarrow B = \dfrac{1}{4}(68) = 17 \\
    \\
\end{gathered} $
We get that the weight of the son is 17 kg.
Therefore, the weight of the father and son is 68 kg and 17 kg.

Note: The pair of linear equation can be solved using elimination method
Using equations (1) and (2)
$\begin{gathered}
  A{\text{ }} + {\text{ }}B = 85 \\
  {\text{ - + + }} \\
  A - 4B = 0 \\
  \underline {\overline {5B = 85} } \\
\end{gathered} $
$ \Rightarrow B = \dfrac{{85}}{5} = 17$
Substituting it in equation (1)
$\begin{gathered}
   \Rightarrow A + 17 = 85 \\
   \Rightarrow A = 85 - 17 \\
   \Rightarrow A = 68 \\
\end{gathered} $
Additional information: A linear system of two equations with two variables is any system that can be written in the form.
$\begin{gathered}
  ax + by = c \\
  dx + ey = f \\
\end{gathered} $
where any of the constants can be zero with the exception that each equation must have at least one variable in it.
Also, the system is called linear if the variables are only to the first power, are only in the numerator and there are no products of variables in any of the equations.