There are an equal number of boys and girls in a class. If 12 girls leave the…

When two groups start out equal in number and one group is reduced by a fixed amount, a condition connecting the two new counts (such as one count becoming a fixed multiple of the other) can be written as a single-variable linear equation and solved directly.

1. Let the original number of boys and the original number of girls each be x, since the class starts with an equal number of boys and girls.

2. After 12 girls leave, the number of girls remaining is x − 12; the number of boys stays x, since no boys leave.

3. The condition states that the boys become twice the remaining girls: x = 2(x − 12).

4. Expand the right-hand side: x = 2x − 24.

5. Rearranging gives x = 24, so there were 24 boys and 24 girls originally.

6. Total number of students = boys + girls = 24 + 24 = 48.

Check: with 24 boys and 24 girls, after 12 girls leave, 12 girls remain and all 24 boys remain. Since 24 is twice 12, the condition holds, confirming a total of 48 students.