Question

10 students of class X took part in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.

Answer 1

Hint: In order to solve this question, first we will assume the number of boys and number of girls as a variable then by question statement we will make the two equations with two variables, and then by solving these equations we will get the answer.

Complete step-by-step solution -

Let the number of girls who took part in the quiz be x.
And let the number of boys who took part in the quiz be y.
Total 10 students took part in the quiz = (number of girls who took part in the quiz) $+$ (number of boys who took part in the quiz)
$$\begin{gathered} x+y=10 \\ x+y-10=0.................\left(1\right) \end{gathered}$$
Also, numbers of girls is 4 more than boys
Number of girls = 4 $+$ number of boys
$$\begin{gathered} x=4+y \\ x-y-4=0.......................\left(2\right) \end{gathered}$$
So, here we have two equations with two variables x and y
$x+y-10=0.................\left(1\right)$
$x-y-4=0.......................\left(2\right)$
Now to evaluate the value of x and y, we will add both the equations, we get
$$\begin{gathered} \Rightarrow x+y+x-y=10+4 \\ \Rightarrow 2x=14 \\ \Rightarrow x=7 \end{gathered}$$
Substitute the value of x in equation (1), we get
$\Rightarrow x+y=10\Rightarrow 7+y=10\Rightarrow y=3$
Hence, the number of girls in the quiz competition is 7 and the number of boys in the quiz competition is 3.

Note: In orders to solve these types of questions read the statement carefully and gather the information as much as possible. In the above question we formulate to linear equations whose solutions can be found either by elimination or substitution method. We have used elimination methods to solve the question. Remember the equations can be solved only when the number of variables is equal to the number of equations.