In a class, the ratio of boys to girls is 11:13. This year, 4 boys and 8 girls join the class, changing the ratio to 4:5. What is the total number of students in the class now?

Explanation

Let the initial number of boys be 11x and girls be 13x. After adding 4 boys and 8 girls, the new numbers become (11x + 4) and (13x + 8), with a ratio of 4:5. Setting up the equation: 5(11x + 4) = 4(13x + 8) leads to 55x + 20 = 52x + 32, which simplifies to 3x = 12, so x = 4. The total strength is (11x + 13x) + 4 + 8 = 24x + 12 = 24*4 + 12 = 108.