Question

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

Answer 1

Hint: First we take a variable as the number of girls of class X took part in a mathematics quiz and another for the number of girls of class X took part in a mathematics quiz.
Then applying the two conditions we will get two equations.
By solving the equations we will get the number of girls of class X who took part in a mathematics quiz & the number of boys of class X took part in a mathematics quiz.

Complete step-by-step answer:
It is given that 10 students of class X took part in a mathematics quiz.
Let, the number of girls of class X took part in a mathematics quiz be \[x\] and the number of boys of class X took part in a mathematics quiz be \[y\]
The total number of students who took part in the mathematics quiz is \[x + y\].
So,\[\;x + y{\rm{ }} = {\rm{ }}10 \ldots ...(1)\]
Mark it as equation (1).
Given that, the number of girls is 4 more than the number of boys.
Thus,\[\;x = y + 4 \ldots ....(2)\]
Let us substitute (2) in (1) we get,
\[y + 4 + y = 10\]
Let us simplify the above equation to find the value of \[y\]we get,
\[2y + 4 = 10\]
\[2y = 10 - 4\]
\[2y = 6\]
\[y = \dfrac{6}{2} = 3\]
Hence we have found that \[y = 3\]
Let us put the value of y in (2) we get,
\[x = 3 + 4 = 7\]
Hence, the number of girls of class X taking part in mathematics is 7 and the number of boys of class X taking part in a mathematics quiz is 3.

Note: If we get two equations with two variables then we can solve it by taking the value of one variable in terms of other from one equation and put it into another. In this problem the more important point is the number of girls is 4 more than boys since it is the first step of substitution we do.