Question

In a class the number of girls is $x$ and that of boys is $y$ . Also the number of girls is $10$ more than the number of boys. The given data in the form of linear equations in two variables also represent it graphically. Find graphically the number of girls if the number of boys is $20$.

Answer 1

Hint: To solve the question we should have the knowledge of the algebraic method which covers the simple operation of mathematics like addition. The first step will be to form the linear equation as per the conditions given in the question. Then we will find the value for the number of girls. This will be represented graphically.

Complete step by step answer:
The question asks us to find the number of girls if the number of boys given is $20$. The other conditions given are that the number of girls are $10$ more than that of the number of boys where girls and boys are x and y respectively. The first step is to form an equation with the help of the condition. So the condition will be written as:
Number of girls = Number of boys + $10$
Now we will substitute the number of the girls and boys with the x$x$ and $y$respectively. On substituting it in the above equation we will get:
$\Rightarrow x=y+10$
The next step will be to represent the above linear equation in the 2-D graph.

The above graph shows the equation $x=y+10$. Now we have found the number of girls when the number of boys is $20$. We will draw a perpendicular from the y- axis representing $20$to the line $x=y+10$, marking it $A$ . From the point of intersection we will draw a line perpendicular on the x- axis.

The perpendicular line from point $A$ intersects the x- axis at$30$, which means that the number of girls are $30$ when the boys are $20$ in number.
$\therefore $ The number of girls if the number of boys is $20$ through graphical representation is $30$.

Note: The above problem has been solved with a graphical method, but we can check the answer by actual calculation. Since the number of girls is the sum of the number of boys and $10$. On writing it mathematically we will get:
$\Rightarrow x=y+10$
Now as per the question, the number of boys is $20$. So we will substitute $y$ with $20$hence finding the number of girls which is:
$\Rightarrow x=20+10$
$\Rightarrow x=30$
So the answer we got is correct, which says the number of girls is $30$.