Question

In a class of 42 students, the number of boys is \[\dfrac{2}{5}\] of girls. How do you find the number of boys and girls in the class?

Answer 1

Hint: We will write the given conditions in mathematical form by using variables and solve them by using elimination methods. We will be getting two linear equations in two variables as have two unknown things in this problem.

Complete step by step answer:
The total strength of the class is 42.
Let the total number of girls be \[x\] and the total number of boys be \[y\].
So, the total strength of the class is equal to the sum of the number of girls and number of boys.
So, we can write it as \[x + y = 42\] -----(1)
And it is given that, total number of boys is equal to \[\dfrac{2}{5}\] of girls.
So, mathematically, we can write it as, \[y = \dfrac{2}{5}x\]
So, that implies that, \[5y = 2x\]
So, we get, \[2x - 5y = 0\] -----(2)
Now, we need to solve these two equations to get the total number of boys and girls.
So, to solve these equations, we have to make the coefficient of any variable the same and eliminate that variable.
So, now let us make coefficients of \[x\] in both equations equal.
So, multiply equation (1) by 2.
\[ \Rightarrow 2x + 2y = 84\]
Now, the coefficients of \[x\] in both equations are the same.
So, now, subtract equation (1) from equation (2)
\[ \Rightarrow 2x - 5y - (2x + 2y) = 0 - 84\]
\[ \Rightarrow 2x - 5y - 2x - 2y = - 84\]
On simplification, we get,
\[ \Rightarrow 7y = 84\]
Divide this whole equation by 7.
\[ \Rightarrow y = \dfrac{{84}}{7} = 12\]
Substitute this value in equation (1)
\[ \Rightarrow x + 12 = 42\]
\[ \Rightarrow x = 42 - 12 = 30\]
So, the number of girls is 30.
And the number of boys is equal to 12.

Note:
We have eliminated the \[x\] and found our answer. But instead, we can also eliminate \[y\] and get the same values. After getting the values, substitute them in the situations or conditions and verify whether the conditions are satisfied or not.
We can use substitution method as well to solve these two equations.