Question

Emile and Gertrude are brother and sister. Emile has twice as many sisters as brothers, and Gertrude has just as many brothers as sisters. How many children are there in this family?

Answer 1

Step-1: Formation of an equation according to question:

Let the number of brother be $p$and sister be $q$
Emile has twice as many sisters as brothers, This means he has $q$ sisters and $(p-1)$ brothers (excluding him)
$\therefore q=2\left(p-1\right)...\left(i\right)$
Gertrude has just as many brothers as sisters, this means she has $p$ brothers and $(q-1)$ sisters (excluding her)
$\therefore p=q-1...\left(ii\right)$

Step-2: Solving equation (i) and (ii):

Putting the equation (i) in equation (ii), we get
$$\begin{gathered} \Rightarrow p=q-1 \\ \Rightarrow p=2(p-1)-1 \\ \Rightarrow 2p-p=2+1 \\ \Rightarrow p=3 \end{gathered}$$
Putting the value of $p=3$ in equation (ii), we get
$$\begin{gathered} \Rightarrow p=q-1 \\ \Rightarrow q=p+1 \\ \Rightarrow q=3+1 \\ =4 \end{gathered}$$
There are three brothers and four sisters
Total number of children $=p+q$
$$\begin{gathered} =3+4 \\ =7 \end{gathered}$$

Hence, the number of children in the family is $7$.