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?
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}.
Let's start by assuming that the total number of students in the class is "x".
According to the given information, 25% of the students walk to school. This means that 0.25x students walk to school. Additionally, there are 6 more students who walk to school. So the total number of students who walk to school is 0.25x + 6.
The remaining students are either taking the bus or coming by car. We know that 20% of the remaining children take the school bus, which means 0.2 * (x - (0.25x + 6)) = 0.2 * (0.75x - 6) students take the bus. There are also 5 more children who take the bus. So the total number of students who take the bus is 0.2 * (0.75x - 6) + 5.
The remaining students come to school by car. We know that there are 19 students who come by car.
Therefore, we can set up the equation:
(x - (0.25x + 6)) - (0.2 * (0.75x - 6) + 5) - 19 = 0
Now, let's solve for x.
x - 0.25x - 6 - 0.15x + 1.2 + 5 - 19 = 0
0.6x - 19.8 = 0
0.6x = 19.8
x = 19.8 / 0.6
x ≈ 33
Therefore, there are approximately 33 children in the class.