in class 9 Number of boys is 5 more than number of girls and 3 times of number of girls is 12 more than double the number of boys find the number of boys and girls
Answers
Answer:-
Let the number of boys be x and number of girls be y.
Given:
Number of boys is 5 more than the number of girls.
⟹ Number of boys = Number of girls + 5
⟹ x = y + 5 -- equation (1)
And,
3 times the number of girls is 12 more than the double of Number of boys.
⟹ 3 * Number of girls = 2 * Number of boys + 12
⟹ 3y = 2x + 12
Substitute the value of x from equation (1).
⟹ 3y = 2(y + 5) + 12
⟹ 3y = 2y + 10 + 12
⟹ 3y - 2y = 22
⟹ y = 22
Substitute the value of y in equation (1).
⟹ x = 22 + 5
⟹ x = 27
Therefore,
- Number of boys = x = 27
- Number of girls = y = 22
Answer :-
★ Number of boys in class = 27
★ Number of girls in class = 22
_____________________
★ Concept :-
Here the concept of Linear Equations in Two Variables has been used. According to this, if the value of one variable is made to depend on the value of another variable, we can find the solutions of the equations. Here first, we need to make equations using the word problem, and then solve it
________________________________
★ Question :-
In class 9 Number of boys is 5 more than number of girls and 3 times of number of girls is 12 more than double the number of boys. Find the number of boys and girls.
★ Solution :-
Given,
~ Case I :-
» Number of boys is 5 more than number of girls
~ Case II :-
» 3 times of number of girls is 12 more than double the number of boys
✒ Let the number of boys in the class be 'x'.
✒ Let the number of girls in the class be 'y'.
Then, applying these values in cases, we get,
~ Case I :-
✏ x = y + 5 .. (i)
~ Case II :-
✏ 3y = 2x + 12 ... (ii)
From equation (i) and equation (ii) we get,
☯ 3y = 2(y + 5) + 12
☯ 3y = 2y + 10 + 12
☯ 3y - 2y = 22
☯ y = 22
Hence, we get the value of y = 22.
Now by applying the value of y, in equation (i), we get,
☯ x = y + 5
☯ x = 22 + 5
☯ x = 27
Hence, the value of x = 27
________________________________
• Number of boys in the class = x = 27
• Number of girls in the class = y = 22
_____________________
★ Verification :-
In order to verify that if our answer is correct or wrong, we must simply apply the values, we got into out equations.
~ Case I :-
=> x = y + 5
=> 27 = 22 + 5 = 27
Clearly, LHS = RHS .
~ Case II :-
=> 3y = 2x + 12
=> 3(22) = 2(27) + 12
=> 66 = 54 + 12 = 66
Clearly, LHS = RHS
Both the conditions satisfy here. Hence our answer is correct
_____________________
★ More to know :-
• Linear Equations are the set of equations formed using constant and variables, which help in solving the word problems where we need to find a value. These can be given as :-
- Linear Equations In One Variable
- Linear Equations In Two Variables
- Linear Equations in Three Variables
• Steps to solve Linear Equations in Two Variables :-
- Substitution Method
- Cross Multiplication Method
- Elimination Method
- Reducing the Pair Method