Question: The number of boys in a class is 4 less than twice the number of girls in the class. If 3 more boys join the class, then the number of girls is 7 less than the number of boys. Find the original number of boys and girls in the class.


A ) 7, 13
B ) 9, 12
C ) 12, 8
D ) 16, 4

Steps to derive

1 Let b represent the original number of boys in the class.

2 Let g represent the original number of girls in the class.

3 Number of boys = 2 (Number of girls) - 4

4 That is: b = 2g - 4 or b - 2g = - 4 - - - (1)

5 Number of girls = (number of boys + 3) - 7

6 That is: g = (b + 3) - 7 or - b + g = - 4 - - - (2)

7 Solve the system of linear equations by using the addition method:

8  b - 2g = - 4
- b + g = - 4
-------------------
       - g = - 8

9 g = 8
 [Solve for g.]

10 b - 2(8) = - 4
 [Substitute the value of g in equation (1).]

11 b = 12

12 So, there are originally 12 boys and 8 girls in the class.



Hence the right answer is Option C

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