In a class, 25% of the students and an additional 6 students walk to school. 20% of the remaining children and an additional 5 children take the school bus to school. The remaining 19 students come to school by car. How many children are there in the class?

Answer 1

Let x be the number of students in the class.
The number of students that walk to school is 25/100 * x + 6 = x/4 + 6.
The number of remaining students is x - x/4 - 6 = (3x - x - 24)/4 = (2x - 24)/4 = x/2 - 6.
The number of students that take the school bus is 20/100 * (x/2 - 6) + 5 = (x/10 - 3) + 5 = x/10 + 2.
The number of students that come to school by car is 19.
Thus, x/4 + 6 + x/10 + 2 + 19 + x/2 - 6 + x/10 = x.
Multiplying through the parentheses, we get x/4 + x/10 + x/2 + x/10 = x - 23.
Combining like terms, we get 5x/20 + 2x/20 + 10x/20 + 2x/20 = x - 23.
Adding, combining like terms, and simplifying, we get 19x/20 = x - 23.
Multiplying through the equation by 20, we get 19x = 20x - 460.
Subtracting 20x from both sides, we get -1x = -460.
Dividing both sides by -1, we get x = 460. Answer: \boxed{460}.