Final answer:
The class consists of 32 girls and 52 boys, found by solving the system of equations derived from the problem statement.
Step-by-step explanation:
In a class of 42 students, the task is to find the number of boys and girls given that the number of boys is 12 fewer than twice the number of girls, and the total sum of boys and girls is 84. Let's define the number of girls as x and the number of boys as 2x - 12. According to the problem, x + (2x - 12) = 84. Solving this equation:
- x + 2x - 12 = 84
- 3x - 12 = 84
- 3x = 96
- x = 32
Therefore, there are 32 girls in the class. To find the number of boys:
- 2x - 12 = 2(32) - 12
- 2x - 12 = 64 - 12
- 2x - 12 = 52
Hence, there are 52 boys in the class.