Question

The number of boys in a school is $120$ more than the number of girls. If there are $980$ students in the school, find the number of boys in the school.

Answer 1

Hint: Here, we are given some information about the relation between the number of boys and number of girls in a school and the total number of students. We assume the number of girls to be “x” and the number of boys to be “y”. From the first condition, we get,
$y=x+120....\left( i \right)$
And, from the second condition, we get,
$x+y=980....\left( ii \right)$
Solving these two equations, we get the value of y which will be the number of boys.

Complete step by step answer:
In this problem, we are given the details about the number of students in a school. It is said that there are both boys and girls in the school and that the number of boys is $120$ more than the number of girls. Also, there are a total of $980$ students in the school. Nothing is mentioned as such of the exact number of boys or girls in the school. This requires the involvement of algebra. We assume the number of girls to be “x” and the number of boys to be “y”. From the first condition, we get,
$y=x+120....\left( i \right)$
And, from the second condition, we get,
$x+y=980....\left( ii \right)$
Subtracting the first equation from the second equation, we get,
$\begin{align}
  & \Rightarrow x=980-\left( x+120 \right) \\
 & \Rightarrow x=-x+860 \\
 & \Rightarrow 2x=860 \\
 & \Rightarrow x=430 \\
\end{align}$
Putting this value of x in the first equation, we get,
$\Rightarrow y=430+120=550$
Therefore, we can conclude that the number of boys in the school is $550$ .

Note: Algebraic problems are very easy when we get to know which quantity is to be taken as a variable. Here, instead of taking the number of girls as x, we could have taken it as y. The answer would have remained the same. Also, we must be careful while solving the equations as most of the problems occur here.